SOLUTION: x/x^2-1+2/x+1=1+1/2x-2

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Question 159353: x/x^2-1+2/x+1=1+1/2x-2
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume your problem is:
x%2F%28%28x%5E2-1%29%29 + 2%2F%28%28x%2B1%29%29 = 1 + 1%2F%28%282x-2%29%29
Factor
x%2F%28%28x-1%29%28x%2B1%29%29 + 2%2F%28%28x%2B1%29%29 = 1 + 1%2F%282%28x-1%29%29
Multiply by common denominator; 2(x+1)(x-1), results:
2x + 2(2(x-1)) = 2(x+1)(x-1) + (x+1)
:
2x + 4x - 4 = 2(x^2-1) + (x + 1)
:
6x - 4 = 2x^2 - 2 + x + 1
:
6x - 4 = 2x^2 + x - 1
:
0 = 2x^2 + x - 6x - 1 + 4
:
0 = 2x^2 - 5x + 3
Factor this to
(2x-3)(x-1) = 0
two solutions:
x = 1
and
2x = 3
x = 3%2F2
x = 1.5
;
The 1st answer, x=1 cannot be a solution, division by 0, therefore;
x = 1.5 is the only solution
:
Check it in the original equation