SOLUTION: Subtract the following 5 over X^2-16 - 3 over X^2-x-12 {{{5/(x^2 - 16)}}} - {{{3/(x^2 - x - 12)}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Subtract the following 5 over X^2-16 - 3 over X^2-x-12 {{{5/(x^2 - 16)}}} - {{{3/(x^2 - x - 12)}}}      Log On


   

Question 85672: Subtract the following
5
over
X^2-16
-
3
over
X^2-x-12
5%2F%28x%5E2+-+16%29 - 3%2F%28x%5E2+-+x+-+12%29
Answer by scianci(186) About Me  (Show Source):
You can put this solution on YOUR website!
You need an LCD. Put your denominators in factored form:
5%2F%28%28x+%2B+4%29%28x+-+4%29%29 - 3%2F%28%28x+-+4%29%28x+%2B+3%29%29
Now it's easy to see that the LCD is (x + 4)(x - 4)(x + 3)
Rewrite each fraction as an equivalent fraction with a denominator of (x + 4)(x - 4)(x + 3):
%285%28x+%2B+3%29%29%2F%28%28x+%2B+3%29%28x+%2B+4%29%28x+-+4%29%29 - %283%28x+%2B+4%29%29%2F%28%28x+%2B+4%29%28x+-+4%29%28x+%2B+3%29%29
Distribute:
%285x+%2B+15%29%2F%28%28x+%2B+3%29%28x+%2B+4%29%28x+-+4%29%29 - %283x+%2B+12%29%2F%28%28x+%2B+4%29%28x+-+4%29%28x+%2B+3%29%29
Combine like terms in the numerators:
%282x+%2B+3%29%2F%28%28x+%2B+3%29%28x+%2B+4%29%28x+-+4%29%29