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 ->  Rational-functions -> 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 188591: 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 x%5E2%2B6x-7 to get %28x%2B7%29%28x-1%29.


Factor x%5E2%2B5x to get x%28x%2B5%29.


Factor 3x%5E2%2B16x%2B5 to get %28x%2B5%29%283x%2B1%29.


Factor 2x%5E2%2B7x-9 to get %282x%2B9%29%28x-1%29.


%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.


So simplifies to %28%28x%2B7%29%283x%2B1%29%29%2F%28x%282x%2B9%29%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 to avoid dividing by zero).