SOLUTION: how do you simplify the rational equation {{{(3)/(x^2+x-2)-(5)/(x^2-x-6)}}}

Algebra ->  Rational-functions -> SOLUTION: how do you simplify the rational equation {{{(3)/(x^2+x-2)-(5)/(x^2-x-6)}}}      Log On


   

Question 738120: how do you simplify the rational equation %283%29%2F%28x%5E2%2Bx-2%29-%285%29%2F%28x%5E2-x-6%29
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
%283%29%2F%28x%5E2%2Bx-2%29-%285%29%2F%28x%5E2-x-6%29

You do what you would normally do if there were no variables in the expression. You already learned this. Find lowest common denominator, change each fraction to equivalent form having the common denominator, perform the addition with the numerators, and then simplify, bring to lowest terms.

Factor those factorable denominators first.
x%5E2%2Bx-2=%28x%2B2%29%28x-1%29 and x%5E2-x-6=%28x%2B2%29%28x-3%29
The necessary lowest common denominator is %28x-1%29%28x-3%29%28x%2B2%29.

APPLY the Common Denominator:


=
=%283%28x-3%29-5%28x-1%29%29%2F%28%28x-1%29%28x-3%29%28x%2B2%29%29
=%283x-3-5x%2B1%29%2F%28%28x-1%29%28x-3%29%28x%2B2%29%29
=%28-2x-2%29%2F%28%28x-1%29%28x-3%29%28x%2B2%29%29
=%28-2%29%28x%2B1%29%2F%28%28x-1%29%28x-3%29%28x%2B2%29%29

Not much more can be done. Best form of answer would be either
highlight%28%28-2x-2%29%2F%28%28x-1%29%28x-3%29%28x%2B2%29%29%29
OR
highlight%28%28-2x-2%29%2F%28theFullyMultipliedCubicPolynomialifyouWantitThatWay%29%29