SOLUTION: Can you show me how to solve for x? ((x-1)/x(x-2)) = 2/3

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Question 174265: Can you show me how to solve for x?
((x-1)/x(x-2)) = 2/3
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
%28x-1%29%2Fx%28x-2%29+=+2%2F3 Expand the denominator of the left side.
%28x-1%29%2F%28x%5E2-2x%29+=+2%2F3 Multiply both sides by 3.
3%28x-1%29%2F%28x%5E2-2x%29+=+2 Multiply both sides by %28x%5E2-2x%29
3x-3+=+2%28x%5E2-2x%29 Expand the right side.
3x-3+=+2x%5E2-4x Subtract 3x from both sides.
-3+=+2x%5E2-7x Add 3 to both sides.
2x%5E2-7x%2B3+=+0 Factor this quadratic equation.
%282x-1%29%28x-3%29+=+0 Apply the zero product rule.
2x-1+=+0 or x-3+=+0, so...
highlight%28x+=+1%2F2%29 or highlight%28x+=+3%29