SOLUTION: Multiply and Simplify: 2x^2-x-3 over x^2-1 * x^2+x-2 over 2x^2 +x-6

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Multiply and Simplify: 2x^2-x-3 over x^2-1 * x^2+x-2 over 2x^2 +x-6      Log On


   

Question 195843: Multiply and Simplify: 2x^2-x-3 over x^2-1 * x^2+x-2 over 2x^2 +x-6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%282x%5E2-x-3%29%2F%28x%5E2-1%29%29%28%28x%5E2%2Bx-2%29%2F%282x%5E2%2Bx-6%29%29 Start with the given expression.


Factor 2x%5E2-x-3 to get %28x%2B1%29%282x-3%29.


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


Factor x%5E2%2Bx-2 to get %28x%2B2%29%28x-1%29.


Factor 2x%5E2%2Bx-6 to get %28x%2B2%29%282x-3%29.


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


1 Simplify.


So %28%282x%5E2-x-3%29%2F%28x%5E2-1%29%29%28%28x%5E2%2Bx-2%29%2F%282x%5E2%2Bx-6%29%29 simplifies to 1.


In other words, %28%282x%5E2-x-3%29%2F%28x%5E2-1%29%29%28%28x%5E2%2Bx-2%29%2F%282x%5E2%2Bx-6%29%29=1 where x%3C%3E-2, x%3C%3E-1, x%3C%3E1, or x%3C%3E3%2F2