SOLUTION: Multiply. {{{(24x^3)/(4x^2-36) * (2x^2+6x)/(16x^2)}}}

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Question 167795This question is from textbook Beginning and Intermediate Algebra
: Multiply. %2824x%5E3%29%2F%284x%5E2-36%29+%2A+%282x%5E2%2B6x%29%2F%2816x%5E2%29 This question is from textbook Beginning and Intermediate Algebra

Found 2 solutions by nerdybill, stanbon:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
%2824x%5E3%29%2F%284x%5E2-36%29+%2A+%282x%5E2%2B6x%29%2F%2816x%5E2%29
Notice we can factor out 8x^2 from numerator and denominator:
%288x%5E2%29%283x%29%2F%284x%5E2-36%29+%2A+%282x%5E2%2B6x%29%2F%288x%5E2%29%282%29
Canceling like-terms:
%283x%29%2F%284x%5E2-36%29+%2A+%282x%5E2%2B6x%29%2F%282%29
.
Now, factoring numerator and denominator:
%283x%29%2F%282x%2B6%29%282x-6%29+%2A+%28x%29%282x%2B6%29%2F%282%29
Canceling like-terms:
%283x%29%2F%282x-6%29+%2A+%28x%29%2F%282%29
%283x%5E2%29%2F%284x-12%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(24x^3)/(4x^2-36) * (2x^2+6x)/(16x^2)
-----------------------
Factor where possible:
(24x^3)/(4(x-3)(x+3)) * (2x(x+3))/(16x^2)
--------------------------
Cancel factors common to a numerator and a denominator,
such as 8, x^2, (x+3)
----------------------------
= (3x)/((x-3)) * (x/(8))
= (3x^2/(8(x-3))
======================
Cheers,
Stan H.