SOLUTION: simplify (x^2+2x-15/x^2-9)/(x^2+6x+5/x^2+4x+3)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: simplify (x^2+2x-15/x^2-9)/(x^2+6x+5/x^2+4x+3)      Log On


   

Question 169800: simplify
(x^2+2x-15/x^2-9)/(x^2+6x+5/x^2+4x+3)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given expression.


%28%28x%5E2%2B2x-15%29%2F%28x%5E2-9%29%29%28%28x%5E2%2B4x%2B3%29%2F%28x%5E2%2B6x%2B5%29%29 Multiply the first fraction %28x%5E2%2B2x-15%29%2F%28x%5E2-9%29 by the reciprocal of the second fraction %28x%5E2%2B6x%2B5%29%2F%28x%5E2%2B4x%2B3%29.


Factor x%5E2%2B2x-15 to get %28x%2B5%29%28x-3%29.


Factor x%5E2-9 to get %28x-3%29%28x%2B3%29.


Factor x%5E2%2B4x%2B3 to get %28x%2B3%29%28x%2B1%29.


Factor x%5E2%2B6x%2B5 to get %28x%2B5%29%28x%2B1%29.


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


1 Simplify.


So simplifies to 1.


In other words, where x%3C%3E-5, x%3C%3E-3, x%3C%3E-1, or x%3C%3E3