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 ->  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


   

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(6294) 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.
Cancel like-factors as indicated, leaving you with:
%28x-5%29%2F%282x%2B3%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given expression


Factor the first numerator (note: if you need help with factoring, check out this solver)


Factor the first denominator


Factor the second numerator


Factor the second denominator


Notice we have these common terms


They divide and cancel out


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


So the expression



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



as a function of y like this

graph of

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.