[Music] in this video we will be discussing multiplication and division of rational algebraic expressions so let's have first our objectives first we have to recall the multiplication and division of fractions and multiply and divide rational algebraic expressions okay how do we multiply fractions so first multiply both the numerators and denominators examples so if i have a over b times c over d then that will become a times c over b times d now remember that your b and d should not be equal to zero that capac equals a zero that will make your fractions undefined lagging now an example so if i have here two over three times three over four so two times three that is six three times four that is twelve and then get the lowest term that is one half okay another example if i have 4 over 5 times 2 over 4 that is 8 over 20 simplify or get the lowest term that is two over five now you can also use cancellations so that is nothing it cancels two and four that will become one and two and then say three so one times one that is one and then one times two that is two okay so put it into one times two that is two and then five times one that is five now in multiplying rational algebraic expressions so same process multiplying fractions so if i have here p over q times r over s so that will become p times r over q times s okay now since i'm denominator not indito iq and s u and s net n should not be equal to zero and remember that your p q r and s d two are already polynomials because we are already in rational algebraic expression so polynomials okay so what are the steps in multiplying rational algebraic expressions so first factor the numerator and denominator after factoring divide or cancel out the common factors and then multiply the remaining terms and simplify if possible let's have an example so i have here a raise is 5 over 10 times 5 over a raised to 3. okay so puedemon apply component i am multiplying fractions okay so numerator and denominator so 8 raised to 5 times 5 that is 5a raised to 5 and then 10 times a raised to 3 that is 10 e raised to 3 and then simplify so you can get the gcf of 5 and 10 or get the lowest term of 5 and 10 that is one half so no need to write one okay and then for the thing the exponent not then we are uh subtracting the exponents of uh the variables with the same basis [Music] denominator okay now this is one way of multiplying rational algebraic expressions another way is factor the numerator and denominator completely so therefore we can have a cube times a squared over two times five times five over eight raised to three okay now one a raised to three and a raise to two okay um okay and then divide or cancel out the common factors so we can now cancel a raise to three and five okay multiply the remaining terms since it is so that is the 2 over 2. now simplify if possible eto nayeon simplified answer not that now let me give you another way or shortcut since uh same basila minus nothing unknown exponent so 5 minus 3 that is a raised to 2. so it's a numerator same as matase 5 and then say 5 and 10 that will become 1 and 2. okay now simplify so a squared times 1 that is a squared and then [Music] okay so in this case long ways on how to multiply rational algebraic expressions another example so i have here 330 b squared over 60 times 4c squared over 15b raised to 4. so by the time by numerator denominator so 30 times 4 that is 120 b squared c squared and then 6 times 15 that is 90 b squared and then c laggy nothing arranged alphabetically and adding variables okay now so therefore we have now 120 over 90 what is the greatest common factor 30 okay so 120 divided by 30 that is 4 1 90 divided by 30 that is three now etona mantiosa exponent with the same basis so four minus two that is two so b squared along so that is b squared and then two minus one that is no need to write one exponent in a one okay so two minus one that is c cinnalang numerator nothing so c so therefore our answer is four c over three b squared another way factor the numerator and denominator completely so our goal is kailang and makaranta in a common factor so since 15 though 2 times 15. so we can cancel out 15 later and then this is six and four tongue two times two attitude squared b squared um b raised to four okay now we can divide or cancel out the common factors so therefore we have we can now cancel 15. we can cancel b squared we can cancel two we can cancel c okay hindi not so therefore multiply the remaining terms so we have two times two that is four and then mainly one is on c and then three times b squared that is three b squared okay another way is b squared okay so tu haser anusha 30 divide 15 and then this is one nalang so no need to write one here now atom b raised to four nothing mean nine is nothing c4 minus two that is two and then saba bacon is a b squared question four minus one that is one so it will so satisfy the guy so it solved nothing multiply two times two that is four c and then three times b squared that is three b squared so meron mankind long options company multiplying rational algebraic expressions okay next now in this case is factor the numerator and denominator completely so we will have three d over three times f minus four by three because three is the common factor [Music] divided without remainder so e23 times f that is three f three times negative four that is negative twelve now d two so the common factor is four four times f that is four f four times negative four that is negative 16. 3d okay so now we can now divide or cancel out the common factors so we have 3d and f minus four now for dinato [Music] okay so let us multiply the remaining terms so therefore that is one and then it's a denominator nothing since so three times d that is 3d so our answer is 1 over 3d another okay so factor the numerator and denominator completely now actually and the two plans are given at the [Music] so we have a plus four a plus four so anu a plus four times a plus four times a plus four over one okay over once a denominator or hindi pudding hindi foreign okay so now we can have a plus four raised to three over one divide not n so that is a plus four raised to three so this will be our final answer now how do we divide fractions dividing fractions okay so a over b divided by c over d and g naga 1 we are getting the reciprocal of our divisor and divisor in second fraction reciprocal so if it's a b n that will become a over b and then d over c okay reciprocal second fraction or young divisor proceeds a multiplication so actually dividing division of fractions but you have to remember your first step get the reciprocal of your divisor so therefore we will have a times d over b times c denominator not in d i b c and d equals zero fasima gigging undefined hey let's have an example so if i have here two over three divided by four over five so i'm getting two over three times five over four and then making multiplication so we will have ten over twelve get the lowest term that is five over 6. rational algebraic expressions okay dividing rational algebraic expressions magicking s over r and then proceed not iso multiplication so we are just going back to the rule to the steps of multiplying rational algebraic expressions so after that in mahogany reciprocal procedure multiplication so therefore we will have p times s over q times r remember that your p q r and s are already polynomials in rational algebraic expressions and since ang denominator undefined let's have an example okay but before that thing steps algebraic expression so same process multiplication let's have an example so i have here a squared minus nine over a minus three divided by a plus three over three a so nothing reciprocal divisor so we will have a squared minus nine over a minus three times okay next so factor the numerator and denominator completely so we will have package and again a plus three and a minus three so this is uh the these are the factors of a squared minus nine okay because this is what ah the difference of two squares so puede mumbali canyon video tutorial about a factoring difference of two squares of playlists over a minus three and then three a over a plus three next can divide or cancel out the common factors since puedenting mahansel ito i n c a plus so we only have three a okay that actually it's three a over one packaging amplifying them and attention three a over one or three a divided by one that is still three a another example okay then this is actually your numerator okay this is your numerator okay so get the reciprocal of your divisors organ x squared plus 2x minus 8 times procedures of multiplication after nothing reciprocal so x squared minus 16 map numeritor next factor the numerator and denominator completely so we will have x plus four x minus two so this is actually factoring off trinomial so foreign video tutorial about factoring a quadratic trinomial okay and then this one difference of two squares to those so i'm getting x plus four x minus four and then another this is um factoring quadratic trinomial so x minus four x plus two okay so we can now divide or cancel out the common factors what are the common factors so we can cancel out x minus four [Music] and then now we can now multiply the remaining terms so therefore we have x minus 2 numerator i x minus 2 and then x plus 4 squared and then it's a denominator we only have x plus two so therefore this is our final answer this is how we sim uh we divide rational algebraic expressions thank you for watching this video i hope you learned something don'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