SOLUTION: Need help solving this equation. x-2/x -x-3/x-6 = 1/x

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Question 171621: Need help solving this equation.
x-2/x -x-3/x-6 = 1/x
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the problem is:
%28%28x-2%29%29%2Fx - %28%28x-3%29%29%2F%28%28x-6%29%29 = 1%2Fx
:
Multiply equation by x(x-6):
x(x-6)*%28%28x-2%29%29%2Fx - x(x-6)*%28%28x-3%29%29%2F%28%28x-6%29%29 = x(x-6)*1%2Fx
Results:
(x-6)(x-2) - x(x-3) = (x-6)
:
x^2 - 8x + 12 - x^2 + 3x = x - 6
:
x^2 - x^2 - 8x + 3x - x = -6 - 12
:
-6x = -18
:
6x = 18
x = 18%2F6
x = 3
:
You can confirm the solution by substituting 3 for x in the original equation