SOLUTION: 2x+1 over (x^2-2x) + 3-x over (5x^2-20) Adding and Subtracting rational expressions. Denominators are in ()

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Question 260945: 2x+1 over (x^2-2x) + 3-x over (5x^2-20)
Adding and Subtracting rational expressions. Denominators are in ()
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
here is the original problem:
%28%282x%2B1%29+%2F+%28x%5E2-2x%29%29+%2B%28%283-x%29+%2F+%285x%5E2-20%29%29+
step 1 - factor the denominators to get
%28%282x%2B1%29%2F%28x%28x-2%29%29%29+%2B+%28%283-x%29%2F%285%28x%5E2-4%29%29%29
notice we have a difference of squares still, so we continue factoring as
%28%282x%2B1%29%2F%28x%28x-2%29%29%29+%2B+%28%283-x%29%2F%285%28x-2%29%28x%2B2%29%29%29
step 2 - the common denominator is 5x(x+2)(x-2). we change the numerators and get a common denominator as

step 3 - expand the numerators to get
%28%2810x%5E2%2B25x%2B10%29%2B+%283x-x%5E2%29%29%2F%285x%28x-2%29%28x%2B2%29%29+
step 4 - combine like terms to get
%289x%5E2+%2B+28x+%2B+10%29%2F%285x%28x-2%29%28x%2B2%29%29