SOLUTION: Solve x+5/x^2+x = 1/x^2+x - x-6/x+1.

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Question 239853: Solve x+5/x^2+x = 1/x^2+x - x-6/x+1.
Answer by algebrapro18(206) About Me  (Show Source):
You can put this solution on YOUR website!
Solve %28x%2B5%29%2F%28x%5E2%2Bx%29+=+1%2F%28x%5E2%2Bx%29+-+%28x-6%29%2F%28x%2B1%29

First we need to factor the denominator of the above problem.

%28x%2B5%29%2F%28x%5E2%2Bx%29+=+1%2F%28x%5E2%2Bx%29+-+%28x-6%29%2F%28x%2B1%29
= %28x%2B5%29%2F%28x%28x%2B1%29%29+=+1%2F%28x%28x%2B1%29%29+-+%28x-6%29%2F%28x%2B1%29

Now we find a common denominator. It will be x(x+1). Now multiply the origonal equation by x(x+1) and simplify.

%28x%2B5%29%2F%28x%28x%2B1%29%29+=+1%2F%28x%28x%2B1%29%29+-+%28x-6%29%2F%28x%2B1%29

%28x%2B5%29%28x%29%28x%2B1%29%2F%28x%28x%2B1%29%29+=+1%28x%29%28x%2B1%29%2F%28x%28x%2B1%29%29+-+%28x%29%28x%2B1%29%28x-6%29%2F%28x%2B1%29
x%2B5+=+1+-+%28x%29%28x-6%29

Now we solve for x.
x+5 = 1 - (x)(x-6)
x+5 = 1 - x^2+6x
x^2-6x+x+5-1 = 0
x^2-5x+4 = 0
(x-4)(x-1) = 0
x = 4 and x = 1