SOLUTION: Perform the operation and simplify: {{{ (x^2-8x+15)/(x^2+12x+32) }}} multiplied by {{{ (x+4)/(x^2-25) }}} Thanks!

Algebra ->  Rational-functions -> SOLUTION: Perform the operation and simplify: {{{ (x^2-8x+15)/(x^2+12x+32) }}} multiplied by {{{ (x+4)/(x^2-25) }}} Thanks!      Log On


   

Question 834778: Perform the operation and simplify:
+%28x%5E2-8x%2B15%29%2F%28x%5E2%2B12x%2B32%29+ multiplied by +%28x%2B4%29%2F%28x%5E2-25%29+
Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Basic idea: Multiply straight across, factor, and simplify by cancelling out common factors between the numerator and denominator.

+%28%28x%5E2-8x%2B15%29%2F%28x%5E2%2B12x%2B32%29%29%28%28x%2B4%29%2F%28x%5E2-25%29%29+

+%28%28%28x-3%29%28x-5%29%29%2F%28x%5E2%2B12x%2B32%29%29%28%28x%2B4%29%2F%28x%5E2-25%29%29+





+%28%28x-3%29%28x-5%29%28x%2B4%29%29%2F%28%28x%2B4%29%28x%2B8%29%28x-5%29%28x%2B5%29%29+





+%28%28x-3%29%28x%2B4%29%29%2F%28%28x%2B4%29%28x%2B8%29%28x%2B5%29%29+





+%28x-3%29%2F%28%28x%2B8%29%28x%2B5%29%29+

+%28x-3%29%2F%28x%5E2%2B13x%2B40%29+

=======================================================

So,

+%28%28x%5E2-8x%2B15%29%2F%28x%5E2%2B12x%2B32%29%29%28%28x%2B4%29%2F%28x%5E2-25%29%29+

simplifies to

+%28x-3%29%2F%28x%5E2%2B13x%2B40%29+