SOLUTION: Adding & Subtracting (5/x) - (4/x+1) + (5/x^2+x) Is the answer (6/x^2+2x-1)

Algebra ->  Algebra  -> Distributive-associative-commutative-properties -> SOLUTION: Adding & Subtracting (5/x) - (4/x+1) + (5/x^2+x) Is the answer (6/x^2+2x-1)      Log On

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Question 171627: Adding & Subtracting
(5/x) - (4/x+1) + (5/x^2+x)
Is the answer (6/x^2+2x-1)
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Add/subtract:
%285%2Fx%29-%284%2F%28x%2B1%29%29%2B%285%2F%28x%5E2%2Bx%29%29 To add/subtract fractions, you need to find the LCD (Lowest Common Denominator), which, in this case, is x%5E2%2Bx+=+x%28x%2B1%29, so you would multiply the first fraction by %28x%2B1%29%2F%28x%2B1%29, and the second fraction by x%2Fx to get:
%285%28x%2B1%29%29%2F%28x%28x%2B1%29%29-%284x%2Fx%28x%2B1%29%29%2B%285%2F%28x%28x%2B1%29%29%29 which simplifies to:
%285x%2B5-4x%2B5%29%2F%28x%28x%2B1%29%29 which further simplifies to:
%28x%2B10%29%2F%28x%28x%2B1%29%29 or highlight%28%28x%2B10%29%2F%28x%5E2%2Bx%29%29