SOLUTION: I am having to multiply the fractions, please show me how to do this. 2x^2-x-3 3x^2-11x-20 ________ x ___________ 3x^2+7x+4 4x^2-9 I really need the help, thanks

Algebra ->  Algebra  -> Exponents-negative-and-fractional -> SOLUTION: I am having to multiply the fractions, please show me how to do this. 2x^2-x-3 3x^2-11x-20 ________ x ___________ 3x^2+7x+4 4x^2-9 I really need the help, thanks       Log On

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Question 85471This question is from textbook algebra
: I am having to multiply the fractions, please show me how to do this.
2x^2-x-3 3x^2-11x-20
________ x ___________
3x^2+7x+4 4x^2-9
I really need the help, thanks
This question is from textbook algebra

Found 2 solutions by Earlsdon, jim_thompson5910:
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply:
%28%282x%5E2-x-3%29%2F%283x%5E2%2B7x%2B4%29%29%28%283x%5E2-11x-20%29%2F%284x%5E2-9%29%29%29 It is often helpful to factor the numerators and the denominators, if possible, and cancel like-factors.
%28%28cross%28%282x-3%29%29cross%28%28x%2B1%29%29%29%2F%28cross%28%283x%2B4%29%29cross%28%28x%2B1%29%29%29%29%28%28cross%28%283x%2B4%29%29highlight%28%28x-5%29%29%29%2F%28highlight%28%282x%2B3%29%29cross%28%282x-3%29%29%29%29 Cancel like-factors as indicated, leaving you with:
%28x-5%29%2F%282x%2B3%29

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
%28%282%2Ax%5E2+-x+-+3%29%2F%283%2Ax%5E2+%2B+7%2Ax+%2B+4%29%29%2A%28%283%2Ax%5E2+-+11%2Ax+-+20%29%2F%284%2Ax%5E2+-+9%29%29 Start with the given expression


%28%28%28x%2B1%29%282%2Ax-3%29%29%2F%283%2Ax%5E2+%2B+7%2Ax+%2B+4%29%29%2A%28%283%2Ax%5E2+-+11%2Ax+-+20%29%2F%284%2Ax%5E2+-+9%29%29 Factor the first numerator (note: if you need help with factoring, check out this solver)


%28%28%28x%2B1%29%282%2Ax-3%29%29%2F%28%28x%2B1%29%283%2Ax%2B4%29%29%29%2A%28%283%2Ax%5E2+-+11%2Ax+-+20%29%2F%284%2Ax%5E2+-+9%29%29 Factor the first denominator


%28%28%28x%2B1%29%282%2Ax-3%29%29%2F%28%28x%2B1%29%283%2Ax%2B4%29%29%29%2A%28%28%283%2Ax%2B4%29%28x-5%29%29%2F%284%2Ax%5E2+-+9%29%29 Factor the second numerator


%28%28%28x%2B1%29%282%2Ax-3%29%29%2F%28%28x%2B1%29%283%2Ax%2B4%29%29%29%2A%28%28%283%2Ax%2B4%29%28x-5%29%29%2F%28%282%2Ax%2B3%29%282%2Ax-3%29%29%29 Factor the second denominator


%28%28highlight%28%28x%2B1%29%29highlight%28%282%2Ax-3%29%29%29%2F%28highlight%28%28x%2B1%29%29highlight%28%283%2Ax%2B4%29%29%29%29%2A%28%28highlight%28%283%2Ax%2B4%29%29%28x-5%29%29%2F%28%282%2Ax%2B3%29highlight%28%282%2Ax-3%29%29%29%29 Notice we have these common terms


%28%28cross%28%28x%2B1%29%29cross%28%282%2Ax-3%29%29%29%2F%28cross%28%28x%2B1%29%29cross%28%283%2Ax%2B4%29%29%29%29%2A%28%28cross%28%283%2Ax%2B4%29%29%28x-5%29%29%2F%28%282%2Ax%2B3%29cross%28%282%2Ax-3%29%29%29%29 They divide and cancel out


Leaving you with this:
%28%28x-5%29%2F%282%2Ax%2B3%29%29


So the expression

%28%282%2Ax%5E2+-x+-+3%29%2F%283%2Ax%5E2+%2B+7%2Ax+%2B+4%29%29%2A%28%283%2Ax%5E2+-+11%2Ax+-+20%29%2F%284%2Ax%5E2+-+9%29%29

simplifies to

%28%28x-5%29%2F%282%2Ax%2B3%29%29


As always, we can verify our answer. We can graph the original expression

%28%282%2Ax%5E2+-x+-+3%29%2F%283%2Ax%5E2+%2B+7%2Ax+%2B+4%29%29%2A%28%283%2Ax%5E2+-+11%2Ax+-+20%29%2F%284%2Ax%5E2+-+9%29%29

as a function of y like this

+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+%28%282%2Ax%5E2+-x+-+3%29%2F%283%2Ax%5E2+%2B+7%2Ax+%2B+4%29%29%2A%28%283%2Ax%5E2+-+11%2Ax+-+20%29%2F%284%2Ax%5E2+-+9%29%29%29+ graph of y=%28%282%2Ax%5E2+-x+-+3%29%2F%283%2Ax%5E2+%2B+7%2Ax+%2B+4%29%29%2A%28%283%2Ax%5E2+-+11%2Ax+-+20%29%2F%284%2Ax%5E2+-+9%29%29

and graph the simplified result

%28%28x-5%29%2F%282%2Ax%2B3%29%29

+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C%28%28x-5%29%2F%282%2Ax%2B3%29%29%29 graph of %28%28x-5%29%2F%282%2Ax%2B3%29%29

Since they produce the same graphs, this means they are equivalent. Since they are equivalent, this means that our answer has been verified.