SOLUTION: Multiply. State any restrictions on the variable x^2+6x-7/x^2+5x times 3x^2+16x+5/2x^2+7x-9

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Multiply. State any restrictions on the variable x^2+6x-7/x^2+5x times 3x^2+16x+5/2x^2+7x-9      Log On


   

Question 189464: Multiply. State any restrictions on the variable


x^2+6x-7/x^2+5x times 3x^2+16x+5/2x^2+7x-9
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given expression


Factor the first numerator


Factor the first denominator


Factor the second numerator


Factor the second denominator


%28%28x%2B7%29%28x-1%29%28x%2B5%29%283x%2B1%29%29%2F%28x%28x%2B5%29%282x%2B9%29%28x-1%29%29 Combine the fractions.


Highlight the common terms


Cancel out the common terms.


%28%28x%2B7%29%283x%2B1%29%29%2F%28x%282x%2B9%29%29 Simplify


%283x%5E2%2B22x%2B7%29%2F%28x%282x%2B9%29%29 FOIL


%283x%5E2%2B22x%2B7%29%2F%282x%5E2%2B9x%29 Distribute


So simplifies to %283x%5E2%2B22x%2B7%29%2F%282x%5E2%2B9x%29


In other words, where x%3C%3E-5, x%3C%3E-9%2F2, x%3C%3E0, or x%3C%3E1 (these are the restrictions)