SOLUTION: I need to divide and simplify this problem. x^2-1 4x-4 ------ / ----- x^2-14x+49 x^2-2x-35 Thank you for your help!!!!!

Algebra ->  Equations -> SOLUTION: I need to divide and simplify this problem. x^2-1 4x-4 ------ / ----- x^2-14x+49 x^2-2x-35 Thank you for your help!!!!!      Log On


   

Question 195802: I need to divide and simplify this problem.
x^2-1 4x-4
------ / -----
x^2-14x+49 x^2-2x-35
Thank you for your help!!!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28x%5E2-1%29%2F%28x%5E2-14x%2B49%29%29%2F%28%284x-4%29%2F%28x%5E2-2x-35%29%29 Start with the given expression.


%28%28x%5E2-1%29%2F%28x%5E2-14x%2B49%29%29%28%28x%5E2-2x-35%29%2F%284x-4%29%29 Multiply the first fraction %28x%5E2-1%29%2F%28x%5E2-14x%2B49%29 by the reciprocal of the second fraction %284x-4%29%2F%28x%5E2-2x-35%29.


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


Factor x%5E2-14x%2B49 to get %28x-7%29%28x-7%29.


Factor x%5E2-2x-35 to get %28x%2B5%29%28x-7%29.


Factor 4x-4 to get 4%28x-1%29.


%28%28x-1%29%28x%2B1%29%28x%2B5%29%28x-7%29%29%2F%284%28x-7%29%28x-7%29%28x-1%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28%28x%2B1%29%28x%2B5%29%29%2F%284%28x-7%29%29 Simplify.


%28x%5E2%2B6x%2B5%29%2F%284%28x-7%29%29 FOIL


%28x%5E2%2B6x%2B5%29%2F%284x-28%29 Distribute


So %28%28x%5E2-1%29%2F%28x%5E2-14x%2B49%29%29%2F%28%284x-4%29%2F%28x%5E2-2x-35%29%29 simplifies to %28x%5E2%2B6x%2B5%29%2F%284x-28%29.


In other words, where x%3C%3E-5, x%3C%3E1, or x%3C%3E7