Adding and Subtracting Rational Algebraic Expressions

[Music] in this video we will recall the concept of adding and subtracting the similar fractions we will also add and subtract rational algebraic expressions with unlike denominators so first how do we add and subtract the similar fractions rational algebraic expressions so in adding and subtracting the similar fractions first we have to find the lcd solve for the numerator and then simplify let us have an example so if i have here 2 over 2 plus 1 over 4 that is equal to so first lcd that is 4 and then 4 divided by 2 at the shaft 4 divided by 2 that is 2 times 2 that is 4 and then 4 divided by four that is one times one that is one okay so four plus one that is five over four or simply if we will try to get its lowest term we will have one and one fourth okay or you can make use of this okay so you just have to multiply this two two times four that is eight and then this one so two times four that is eight and then one times two that is two okay and then we will add eight and two so we will have eight plus two over eight so after nothing to multiply so we will multiply these two that will be our denominator and then that is eight plus two so we will have ten over eight so if kuni method so a two international thing butterfly method now so ebik sabihin if you&#39;re gonna use the lcd or you can make use of the butterfly method you can still get the same answer let&#39;s have another so again i have 2 over 2 minus 1 over 6 so that is what is the lcd that is 6 so 6 divided by two that is three times two that is six and then six divided by six one times one that is one so since this is already subtraction that is six minus one so that we will have five over six now since this is already the lowest term then therefore five over six is our final answer next let us use the butterfly method so multiply first two times six that is 12 multiply 2 times 6 that is 12 1 times 2 that is 2 and then we will subtract so 12 minus 2 that is 10 over 12 so we will have get the lowest term that is now how do we add and subtract rational expressions with unlike denominators so pakistan okay like denominators so you just have to copy the denominator in this case and then after that we will find the lcd next is we will write the equivalent expression of each rational expression using the lcd and the last one proceeds add and subtract and then we will keep or copy the lcd let&#39;s have an example so if i have here five over eight m squared and raised to four plus two over six m cube n okay so uh denominators so what is our first step factor the denominators completely so who need nothing in your denominators and rational expressions we have eight m squared and raised to four and then six m cube n so denominators and then we will try to factor so this is uh this can be written in exponential notation which is 2 cube or 2 raised to 3 okay and then m squared and then n raised to 4 okay so later i will explain company lcd unlike denominator style and then for 6 so we have 2 times 3 so um okay and then m cube and then n now factors degree sodium okay and then for m we will get m raised to three because matasto and then for n we will get n raised to four okay so in finding the lcd we will get the highest degree of the exponents and then we will uh simplify so we now have 2 cube 3 m raised to 3 and n raised to 4 okay so let us find the lcd let us simplify so i have here 2 cube 2 cube is 8 and then 3 m raised to 3 times n raised to 4. so let us solve 8 times 3 that is 24 and then just copy the literal coefficient so we have m raised to 3 and raised to 4. so therefore our lcd is 24 m raised to 3 and raised to 4. so we now have our lcd let&#39;s proceed to the next step which is we will be writing the equivalent fractions of the given rational expressions so we will have 24 divided by eight that is three okay now why do i have m here 24 divided by eight that is three next m not n we have three minus two so ilanalang that is one so since hapagan exponent not in a one hindi and nothing now for our n we have four minus four so we will now have n raised to zero yo so we have 5 times 3 that is 15 m so so 5 times 3 m that is 15 m okay so cancel we have 24 divided by six that is four okay so that is four now see m net n3 minus three that is m raised to zero and that is equal to one so no need to write that okay and then four minus one this is one okay so that&#39;s why we have here n raised to three so nothing fork is 24 divided by six that is four and then mafa hansel outnato and then four minus one that is n raised to three okay so let us simplify now so two times four that is eight and raised to three okay so we know ge got the uh equivalent fractions of this rational expression so an x we can now add the numerators and then we will just copy their lcd okay so what is our numerator for the first expression we have 15 m and then for our second expression we have eight n cubed since indeed so this will be our final answer now remember keep the lcd so our lcd is 24 m raised to 3 and raised to 4. let&#39;s have the second example so i have here 2y over 5x squared plus 3x over 4xy so factor the denominators completely so we will get the denominators 5x squared and 4xy so so for 5x squared we have 5 times x squared for 4xy we have 4 times x times y okay so we will get the highest uh degree of the exponent so cone it four five five raised to one so well so that is five one four four and then x x squared and then so y y raised to one okay since that is the highest okay so we will now uh multiply all the factors so we will have five times four times x squared times y so find the lcd let us simplify so that is 20 x squared y so we now have our lcd next is we will write the equivalent fraction so since parehana lcd we have 20x squared y and 20x squared y for our rational expressions now it&#39;s assaulted in adidas okay so balika nathaniel okay so our lcd again is 20 x squared y by the way okay so okay so again cancel so 20 divided by five that is four okay x squared outnayan and then y since mandito so copy not in cy okay so we have 4y now simplify 2 times 4 that is 8 and then y times y that is y squared so we will have 8y squared next 20 divided by four that is five at all and then x naught and two minus one since this is one the bar so that is one nalang okay but no need to write one for our exponent okay and then for our y this will be cancelled okay so we now have five x so three times five that is fifteen and then the lawyer x naught and we will multiply so we will add the exponents 1 plus 1 so that is x squared so 15 x squared okay so let&#39;s proceed to the last step we will add the numerators and keep the lcd so 8y squared plus 15x squared okay and then keep the lcds in same name and silas so 20x squared y and then 8y squared plus 15x squared okay hindi similar terms okay y squared ato i x squared so this will be our final answer next i have 4x over x squared minus 25 minus 5 over x minus 5. so first factor the denominators completely so we will get x squared minus 25 and x minus 5. so what are the factors of x squared minus 25 okay so this is an example of a difference of two squares okay so factor time and difference of two squares maggie sum and differentia okay so we now have x plus five and x minus five and then for x minus five good number okay now so nothing on highest exponent so for x plus five so etosha and then for x minus five since para huna mancillon raised to one lamb so x minus five gohan and tainan is done okay so therefore we will multiply or we we now have x plus five times x minus five okay so let us get the lcd so our lcd is x plus five times x minus five okay now so write the equivalent fractions okay so we will have this okay so you given okay our lcd is x plus five x minus five okay now eto equivalent uh previous slide this is equivalent to x plus 5 and x minus 5 right so therefore raised to 0 and that now for our next given the denominator so since x minus 5 x plus 5 so you know times nothing guy 5 so we now have 5 x plus 5 times 5 five so e big sub hen we will have five x plus twenty five okay so eto for x long shakas now we will subtract okay so subtract the numerators and keep the lcd so this is already subtraction now remember you just have to copy so 4x and then minus 5x plus 25 minus 5x and then minus 25. okay remembering operations so from positive negative positive negative now we can now simplify so we can combine for x and 5x since they are similar terms so 4x minus 5x we have negative x minus 25 bucket negative x because negative five positive four minus five that is negative one and hindi nothing needs to always remember that so therefore our final answer is negative x minus 25 all over x plus five times x minus five thank you for watching this video i hope you learned something don&#39;t forget to like subscribe and hit the notification bell for updated ko for more video tutorials this is your guide in learning your math lessons your walmart channel

[Music] in this video we will recall the concept of adding and subtracting the similar fractions we will also add and subtract rational algebraic expressions with unlike denominators so first how do we add and subtract the similar fractions rational algebraic expressions so in adding and subtracting the similar fractions first we have to find the lcd solve for the numerator and then simplify let us have an example so if i have here 2 over 2 plus 1 over 4 that is equal to so first lcd that is 4 and then 4 divided by 2 at the shaft 4 divided by 2 that is 2 times 2 that is 4 and then 4 divided by four that is one times one that is one okay so four plus one that is five over four or simply if we will try to get its lowest term we will have one and one fourth okay or you can make use of this okay so you just have to multiply this two two times four that is eight and then this one so two times four that is eight and then one times two that is two okay and then we will add eight and two so we will have eight plus two over eight so after nothing to multiply so we will multiply these two that will be our denominator and then that is eight plus two so we will have ten over eight so if kuni method so a two international thing butterfly method now so ebik sabihin if you&amp;#39;re gonna use the lcd or you can make use of the butterfly method you can still get the same answer let&amp;#39;s have another so again i have 2 over 2 minus 1 over 6 so that is what is the lcd that is 6 so 6 divided by two that is three times two that is six and then six divided by six one times one that is one so since this is already subtraction that is six minus one so that we will have five over six now since this is already the lowest term then therefore five over six is our final answer next let us use the butterfly method so multiply first two times six that is 12 multiply 2 times 6 that is 12 1 times 2 that is 2 and then we will subtract so 12 minus 2 that is 10 over 12 so we will have get the lowest term that is now how do we add and subtract rational expressions with unlike denominators so pakistan okay like denominators so you just have to copy the denominator in this case and then after that we will find the lcd next is we will write the equivalent expression of each rational expression using the lcd and the last one proceeds add and subtract and then we will keep or copy the lcd let&amp;#39;s have an example so if i have here five over eight m squared and raised to four plus two over six m cube n okay so uh denominators so what is our first step factor the denominators completely so who need nothing in your denominators and rational expressions we have eight m squared and raised to four and then six m cube n so denominators and then we will try to factor so this is uh this can be written in exponential notation which is 2 cube or 2 raised to 3 okay and then m squared and then n raised to 4 okay so later i will explain company lcd unlike denominator style and then for 6 so we have 2 times 3 so um okay and then m cube and then n now factors degree sodium okay and then for m we will get m raised to three because matasto and then for n we will get n raised to four okay so in finding the lcd we will get the highest degree of the exponents and then we will uh simplify so we now have 2 cube 3 m raised to 3 and n raised to 4 okay so let us find the lcd let us simplify so i have here 2 cube 2 cube is 8 and then 3 m raised to 3 times n raised to 4. so let us solve 8 times 3 that is 24 and then just copy the literal coefficient so we have m raised to 3 and raised to 4. so therefore our lcd is 24 m raised to 3 and raised to 4. so we now have our lcd let&amp;#39;s proceed to the next step which is we will be writing the equivalent fractions of the given rational expressions so we will have 24 divided by eight that is three okay now why do i have m here 24 divided by eight that is three next m not n we have three minus two so ilanalang that is one so since hapagan exponent not in a one hindi and nothing now for our n we have four minus four so we will now have n raised to zero yo so we have 5 times 3 that is 15 m so so 5 times 3 m that is 15 m okay so cancel we have 24 divided by six that is four okay so that is four now see m net n3 minus three that is m raised to zero and that is equal to one so no need to write that okay and then four minus one this is one okay so that&amp;#39;s why we have here n raised to three so nothing fork is 24 divided by six that is four and then mafa hansel outnato and then four minus one that is n raised to three okay so let us simplify now so two times four that is eight and raised to three okay so we know ge got the uh equivalent fractions of this rational expression so an x we can now add the numerators and then we will just copy their lcd okay so what is our numerator for the first expression we have 15 m and then for our second expression we have eight n cubed since indeed so this will be our final answer now remember keep the lcd so our lcd is 24 m raised to 3 and raised to 4. let&amp;#39;s have the second example so i have here 2y over 5x squared plus 3x over 4xy so factor the denominators completely so we will get the denominators 5x squared and 4xy so so for 5x squared we have 5 times x squared for 4xy we have 4 times x times y okay so we will get the highest uh degree of the exponent so cone it four five five raised to one so well so that is five one four four and then x x squared and then so y y raised to one okay since that is the highest okay so we will now uh multiply all the factors so we will have five times four times x squared times y so find the lcd let us simplify so that is 20 x squared y so we now have our lcd next is we will write the equivalent fraction so since parehana lcd we have 20x squared y and 20x squared y for our rational expressions now it&amp;#39;s assaulted in adidas okay so balika nathaniel okay so our lcd again is 20 x squared y by the way okay so okay so again cancel so 20 divided by five that is four okay x squared outnayan and then y since mandito so copy not in cy okay so we have 4y now simplify 2 times 4 that is 8 and then y times y that is y squared so we will have 8y squared next 20 divided by four that is five at all and then x naught and two minus one since this is one the bar so that is one nalang okay but no need to write one for our exponent okay and then for our y this will be cancelled okay so we now have five x so three times five that is fifteen and then the lawyer x naught and we will multiply so we will add the exponents 1 plus 1 so that is x squared so 15 x squared okay so let&amp;#39;s proceed to the last step we will add the numerators and keep the lcd so 8y squared plus 15x squared okay and then keep the lcds in same name and silas so 20x squared y and then 8y squared plus 15x squared okay hindi similar terms okay y squared ato i x squared so this will be our final answer next i have 4x over x squared minus 25 minus 5 over x minus 5. so first factor the denominators completely so we will get x squared minus 25 and x minus 5. so what are the factors of x squared minus 25 okay so this is an example of a difference of two squares okay so factor time and difference of two squares maggie sum and differentia okay so we now have x plus five and x minus five and then for x minus five good number okay now so nothing on highest exponent so for x plus five so etosha and then for x minus five since para huna mancillon raised to one lamb so x minus five gohan and tainan is done okay so therefore we will multiply or we we now have x plus five times x minus five okay so let us get the lcd so our lcd is x plus five times x minus five okay now so write the equivalent fractions okay so we will have this okay so you given okay our lcd is x plus five x minus five okay now eto equivalent uh previous slide this is equivalent to x plus 5 and x minus 5 right so therefore raised to 0 and that now for our next given the denominator so since x minus 5 x plus 5 so you know times nothing guy 5 so we now have 5 x plus 5 times 5 five so e big sub hen we will have five x plus twenty five okay so eto for x long shakas now we will subtract okay so subtract the numerators and keep the lcd so this is already subtraction now remember you just have to copy so 4x and then minus 5x plus 25 minus 5x and then minus 25. okay remembering operations so from positive negative positive negative now we can now simplify so we can combine for x and 5x since they are similar terms so 4x minus 5x we have negative x minus 25 bucket negative x because negative five positive four minus five that is negative one and hindi nothing needs to always remember that so therefore our final answer is negative x minus 25 all over x plus five times x minus five thank you for watching this video i hope you learned something don&amp;#39;t forget to like subscribe and hit the notification bell for updated ko for more video tutorials this is your guide in learning your math lessons your walmart channel

Transcript for:Adding and Subtracting Rational Algebraic Expressions

Transcript for:
Adding and Subtracting Rational Algebraic Expressions