[Music] in this video we will recall addition and subtraction of similar fractions and we will add and subtract rational algebraic expressions with like denominators so we will focus on rational algebraic expressions with like denominators so how do we add and subtract similar fractions so in adding similar fractions we will add or subtract the numerator then we will copy the denominator next is simplify if possible so pakistan have nothing simplified antenatal nothing lowest term okay so let us have an example so i have two fourths plus one fourth so two plus one uh that is three and then copy the denominator so we have three fourths another example i have four minus two so that is two and then copy the denominator that is six now we can still get the lowest term of two over six using the gcf of 2 so 2 divided by 2's that is 1 and then 6 divided by 2 that is 3 so therefore the lowest term is one thirds next so i have 3 over 5 plus 1 over 5 so we have four and then five okay so the answer is four fifths next three minus two that is one and then copy the denominator that is six so one over six so how do we add and subtract rational expressions with like denominators rational expressions denominators okay so how do we do this so first add or subtract the numerator next copy the common denominator next is factor the numerator and cancel out or divide the common factor then simplify let's have an example or illustrate a representation so if i have here a over c plus b over c so we will add the numerator and then step so we will have a plus b over c now if you have subtraction among so you just have to subtract a minus b over c now remember that your c should not be equal to zero undefined okay and then remember also that your a over c and b over c should be rational expressions okay let's have an example so i have here 2a over 4b plus 3 over 4b so first step add the numerator so we will have two a plus three next copy the common denominator what is the denominator so since so we will have four b now factor the numerator if possible effector if not then proceed to the next step which is simplify so since wala naman time for out so therefore 2a plus 3 over 4b is our final answer next i have 10 c over 13 plus 6 c over 13 so we will have add the numerator so we will get 26 26c because 10c plus 16c is equal to 26c and then copy the common denominator that is 13 so we will have 26c over thirteen what is the next step factor the numerator factor in 2016 foreign so we can have 13 times 2c okay because it's 13 times so that is 26 and then c over 13 so now we can now fact a cancel out or divide 13. so 13 and you 30 nothing's a denominator so we will simplify what's left is 2c next i have 8 d minus three over nine plus four d plus twelve all over nine so next first step is add the numerator so we will have eight d minus three pakista mahind lag nathan shah ecohome by nathan plus 4d plus 12 okay and then copy the common denominator which is nine next step is we will combine similar terms so mako combine tied and similar terms since pare hotend so eight plus four that is 12d and then negative three ato paragon constant and 12 that is nine so therefore we will have 12d plus nine and then copy your denominator okay now next is you have to factor the numerator so i said nothing should putting a factor by three okay so we can factor this uh binomial using three okay so we will have four d plus three because three times four that is 12d and then three times three that is nine okay all over nine okay now we can cancel out three and nine this is one and this is three so therefore simplify your answer we will have four d plus three over 3 next so i have here 9x squared over 3x minus 5 minus 25 all over 3x minus five so first subtract the numerator okay in subtracting the numerator since nasa's subtraction we are changing the signs of our subtrahend okay [Music] we will have 9x squared ato young positive 25 okay so remember that in subtracting change the sign of your subtrahend so hong meron kapang okay next copy the common denominator so i have here three x minus five so we will copy next is factor okay so 9x squared minus 25 is an example of difference of two squares okay so therefore uh nothing is sum and difference okay so plug in squared nothing thought in square not n so we will have 3x plus 5 and 3x minus 5 because 3 times 3 that is 9 x and x x squared and then 5 times 5 that is 25 and then copy the denominator now after uh you factor the numerator and the next step cancel okay you can now cancel or divide so what's left is we have 3x plus 5 next so i have here 9y squared all over y minus 2 minus y squared plus 16y all over y minus two so first step subtract the numerator since attraction so we will change the signs of our subtrahend so atoms and then minus y squared minus 16 y so since an operation anatomy subtraction change the sign of your subtrahend the signs of all your subtrahend so and then copy your common denominator so we have y minus two so now we will combine similar terms okay so since para silang y squared so nine minus one that is eight y squared minus sixteen y so indeed nothing to putting a combined on because this is only on the uh first degree okay and then copy your denominator now factor so so by eight okay by eight wise factor okay okay and then 8y times y so that is 8y squared and then 8y times negative 2 that is negative 16y so copy the denominator we can now cancel y minus two so therefore we will have eight y next i have h squared plus eight h minus fifteen all over three h squared minus nine inch minus four h plus six all over three h squared minus nine each so first step subtract the numerator so i'm gagawina then copy your so we will change the sign of our subtrahend so happy your first uh your mean event and then positive negative positive negative okay and then copy your the common denominator which is your three h squared minus nine h so we will now have combine similar terms h squared so we will have eight minus four so we will have h squared plus four h because eight minus four that is 4 and then negative 15 minus 6 so that is negative 21 okay and then copy the denominator which is 3 h squared minus 9 h now factor so i this is an example of a general trinomial okay so haha haha now factoring 21. okay so we will have h plus seven and times h minus three ok okay so now we have h plus seven times h minus three all over three h times h minus three so by three h because this is the common factor okay common monomial factor so three h times h that is three h squared and then three h times negative three that is negative nine each so anunga govinda natin ngayan we can now cancel h minus three so what is our answer so we have h plus seven all over three h 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 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