SOLUTION: Solve equation: (x+1/x-1) + (2/x)= (x/x+1) How do I solve this?

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Question 202333: Solve equation:
(x+1/x-1) + (2/x)= (x/x+1)
How do I solve this?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve equation:
(x+1/x-1) + (2/x)= (x/x+1)
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Multiply thru by x(x-1)(x+1) to get:
x(x+1)^2 + 2(x-1)(x+1) = x^2(x-1)
x(x^2 + 2x + 1) + 2(x^2-1) = x^3-x^2
x^3 + 2x^2 + x + 2x^2-2 = x^3-x^2

5x^2 + x -2 = 0
x = [-1 +- sqrt(1 - 4*5*-2)]/10
x = [-1 +- sqrt(41)]/10
==========================================
Cheers,
Stan H.