SOLUTION: I have a problem that says "Simplify: x over x^2+5x+6 minus 2 over x^2+3x+2 I knew how to do this at one time but having been out of Algebra for a while I've forgotten. Could you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have a problem that says "Simplify: x over x^2+5x+6 minus 2 over x^2+3x+2 I knew how to do this at one time but having been out of Algebra for a while I've forgotten. Could you       Log On


   

Question 86485: I have a problem that says "Simplify: x over x^2+5x+6 minus 2 over x^2+3x+2
I knew how to do this at one time but having been out of Algebra for a while I've forgotten. Could you please help? Thanks
Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
Simplifying rational expressions:
%28x%29%2F%28x%5E2%2B5x%2B6%29-%282%29%2F+%28x%5E2%2B3x%2B2%29%29
.
%28x%29%2F%28x%2B3%29%28x%2B2%29-%282%29%2F+%28x%2B1%29%28x%2B2%29%29%29 [factor]
.
[cross-multiply]
.
%28x%29%28x%2B1%29%2F%28x%2B3%29-%282%29%28x%2B3%29%2F+%28x%2B1%29%29%29%29 [cancel wherever possible]
.
%28x%5E2%2Bx%29%2F%28x%2B3%29-%282x%2B6%29%2F+%28x%2B1%29%29%29 [simplify the numerators and eliminate the denominator]
.
%28x%5E2%2Bx%29-%282x%2B6%29%29%29%29[place the numerator over the LCD (x+3)(x+2)(x+1)]
.
%28x%5E2%2Bx+-2x-6%29%2F%28x%2B3%29%28x%2B2%29%28x%2B1%29%29%29%29 [combine like-terms in the numerator]
.
%28x%5E2+-x-6%29%2F%28x%2B3%29%28x%2B2%29%28x%2B1%29%29%29%29 [simplify]
.
%28%28x+-3%29%28x%2B2%29%29%2F%28x%2B3%29%28x%2B2%29%28x%2B1%29%29%29%29 [factor the numerator if possible]
.
%28x+-3%29%2F%28x%2B3%29%28x%2B1%29%29%29%29 [cancel wherever possible]