SOLUTION: ((x^2-1)/(x^2+4x+4))/((5x+5)/(x^2+11x+18))

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: ((x^2-1)/(x^2+4x+4))/((5x+5)/(x^2+11x+18))      Log On


   

Question 251463: ((x^2-1)/(x^2+4x+4))/((5x+5)/(x^2+11x+18))
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28x%5E2-1%29%2F%28x%5E2%2B4x%2B4%29%29%2F%28%285x%2B5%29%2F%28x%5E2%2B11x%2B18%29%29 Start with the given expression.


%28%28x%5E2-1%29%2F%28x%5E2%2B4x%2B4%29%29%28%28x%5E2%2B11x%2B18%29%2F%285x%2B5%29%29 Multiply the first fraction %28x%5E2-1%29%2F%28x%5E2%2B4x%2B4%29 by the reciprocal of the second fraction %285x%2B5%29%2F%28x%5E2%2B11x%2B18%29.


Factor x%5E2-1 to get %28x-1%29%2A%28x%2B1%29.


Factor x%5E2%2B4x%2B4 to get %28x%2B2%29%28x%2B2%29.


Factor x%5E2%2B11x%2B18 to get %28x%2B9%29%2A%28x%2B2%29.


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


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28%28x-1%29%28x%2B9%29%29%2F%285%28x%2B2%29%29 Simplify.


%28x%5E2%2B8x-9%29%2F%285%28x%2B2%29%29 FOIL


%28x%5E2%2B8x-9%29%2F%285x%2B10%29 Distribute


So %28%28x%5E2-1%29%2F%28x%5E2%2B4x%2B4%29%29%2F%28%285x%2B5%29%2F%28x%5E2%2B11x%2B18%29%29 simplifies to %28x%5E2%2B8x-9%29%2F%285x%2B10%29.


In other words,