SOLUTION: Do the operation and simplify the answer. {{{(5x^2+21x+4)/(x^2-16)}}} / {{{(5x+1)/(x-2)}}} I need help with this please.

Algebra ->  Expressions-with-variables -> SOLUTION: Do the operation and simplify the answer. {{{(5x^2+21x+4)/(x^2-16)}}} / {{{(5x+1)/(x-2)}}} I need help with this please.      Log On


   

Question 294481: Do the operation and simplify the answer.
%285x%5E2%2B21x%2B4%29%2F%28x%5E2-16%29 / %285x%2B1%29%2F%28x-2%29
I need help with this please.
Found 2 solutions by unlockmath, richwmiller:
Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
This %285x%5E2%2B21x%2B4%29%2F%28x%5E2-16%29 / %285x%2B1%29%2F%28x-2%29 can be written as follows:
{(5x^2+21x+4)/(x^2-16)} multiplied by {(x-2)/(5x+1)} The first fraction can be rewritten as:
{(5x+1)(x+4)/(x-4)(x+4)}times{(x-2)/(5x+1)} Notice the (5x+1) and the (x+4)cancels out to leave us with:
(x-2)/(x-4)
Make sense?
RJ
There's a book I wrote on the basics you'd like:
www.math-unlock.com

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
%28%285x%5E2%2B21x%2B4%29%2F%28x%5E2-16%29%29+%2F+%28%285x%2B1%29%2F%28x-2%29%29
This all reduces to (x-2)/(x-4)
First division is the same as multiplication by the reciprocal
%285x%5E2%2B21x%2B4%29%2F%28x%5E2-16%29+%2A%28x-2%29%2F+%285x%2B1%29
Next factor (x^2-16)=(x-4)(x+4)
Factor 5x^2+21x+4 = (5x+1)*(x+4)
Cancel out (5x+1) and (x+4)
and we have (x-2)/(x-4)