SOLUTION: {{{(2)/(x+3)+(5)/(3-x)-(6)/(x^2-9)}}}

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: {{{(2)/(x+3)+(5)/(3-x)-(6)/(x^2-9)}}}      Log On

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Question 135286: %282%29%2F%28x%2B3%29%2B%285%29%2F%283-x%29-%286%29%2F%28x%5E2-9%29
Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
%282%29%2F%28x%2B3%29%2B%285%29%2F%283-x%29-%286%29%2F%28x%5E2-9%29

First note that 3-x=-x%2B3=-%28x-3%29, so you can re-write the entire expression as:

%282%29%2F%28x%2B3%29-%285%29%2F%28x-3%29-%286%29%2F%28x%5E2-9%29

Second note that x%5E2-9 is the difference of two squares and factors to %28x%2B3%29%28x-3%29. Since this is just the product of the other two denominators, x%5E2-9 is the lowest common denominator.

Now you can write:
%282%28x-3%29-5%28x%2B3%29-6%29%2F%28x%5E2-9%29

Now all you need to do is clear the parentheses in the numerator and collect like terms.