SOLUTION: Can someone help me simplify this rational expression? X-2/x^2-4 + 2/x+2 First I look for the lcd, then I build up the fractions and get: x-2/(x+2)(x-2) + 2x-4/(x-2)(x+2) and t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can someone help me simplify this rational expression? X-2/x^2-4 + 2/x+2 First I look for the lcd, then I build up the fractions and get: x-2/(x+2)(x-2) + 2x-4/(x-2)(x+2) and t      Log On


   

Question 607640: Can someone help me simplify this rational expression? X-2/x^2-4 + 2/x+2
First I look for the lcd, then I build up the fractions and get: x-2/(x+2)(x-2) + 2x-4/(x-2)(x+2) and the I am unclear what to do as the answe comes out to: 3/x+2 but I do not understand how they came up with that answer. Please help!
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-2%29%2F%28x%5E2-4%29+%2B+2%2F%28x%2B2%29
%28x-2%29%2F%28%28x%2B2%29%28x-2%29%29+%2B+2%2F%28x%2B2%29
%28x-2%29%2F%28%28x%2B2%29%28x-2%29%29+%2B+%282%2F%28x%2B2%29%29%28%28x-2%29%2F%28x-2%29%29
%28x-2%29%2F%28%28x%2B2%29%28x-2%29%29+%2B+%282x-4%29%2F%28%28x%2B2%29%28x-2%29%29
Everything you've done so far is correct. The reason you found the LCD and changed the second fraction so it had the LCD for a denominator was so you could add the fractions. So that is the next step, add:
%283x-6%29%2F%28%28x%2B2%29%28x-2%29%29
Now, as usual when you have a fraction for an answer, we reduce the fraction if possible. To reduce a fraction you cancel common factors in the numerator and denominator. To cancel common factors you have to have factors, first. The denominator is already/still factored. In the numerator we have a GCF of 3 we can factor out:
%283%28x-2%29%29%2F%28%28x%2B2%29%28x-2%29%29
And lo and behold, we have a common factor of (x-2) we can cancel:
%283%2Across%28%28x-2%29%29%29%2F%28%28x%2B2%29%2Across%28%28x-2%29%29%29
leaving:
3%2F%28x%2B2%29
which will not reduce further.