SOLUTION: multiply or divide as indicated x^2-5x+6/x^2+x-6 * x^2-4/x^2-x-6 a)x-3/x+2 b)x+2/x-3 c)x-2/x+3 d)x+2/x+3

Algebra ->  Equations -> SOLUTION: multiply or divide as indicated x^2-5x+6/x^2+x-6 * x^2-4/x^2-x-6 a)x-3/x+2 b)x+2/x-3 c)x-2/x+3 d)x+2/x+3      Log On


   

Question 147743: multiply or divide as indicated
x^2-5x+6/x^2+x-6 * x^2-4/x^2-x-6
a)x-3/x+2
b)x+2/x-3
c)x-2/x+3
d)x+2/x+3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28x%5E2-5x%2B6%29%2F%28x%5E2%2Bx-6%29%29%28%28x%5E2-4%29%2F%28x%5E2-x-6%29%29 Start with the given expression.


%28%28%28x-2%29%2A%28x-3%29%29%2F%28x%5E2%2Bx-6%29%29%28%28x%5E2-4%29%2F%28x%5E2-x-6%29%29 Factor x%5E2-5x%2B6 to get %28x-2%29%2A%28x-3%29.


Factor x%5E2%2Bx-6 to get %28x%2B3%29%2A%28x-2%29.


Factor x%5E2-4 to get %28x-2%29%2A%28x%2B2%29.


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


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28x-2%29%2F%28x%2B3%29 Simplify.


So %28%28x%5E2-5x%2B6%29%2F%28x%5E2%2Bx-6%29%29%28%28x%5E2-4%29%2F%28x%5E2-x-6%29%29 simplifies to %28x-2%29%2F%28x%2B3%29.


In other words, where x%3C%3E-3, x%3C%3E-2, or x%3C%3E2