SOLUTION: x/2 + 1/x-1 = x/x-1 thank you for the help for solving this equation.

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Question 290748: x/2 + 1/x-1 = x/x-1
thank you for the help for solving this equation.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
%28x%2F2%29%2B%281%2F%28x-1%29%29+=+x%2F%28x-1%29 The lowest common denominator (LCD) is: 2%28x-1%29, so...
%28x%28x-1%29%2F2%28x-1%29%29%2B2%2F%282%28x-1%29%29+=+2x%2F%282%28x-1%29%29 Multiply through by 2%28x-1%29 to clear the fractions.
x%28x-1%29%2B2+=+2x Simplify.
x%5E2-x%2B2+=+2x Subtract 2x from both sides.
x%5E2-3x%2B2+=+0 Solve by factoring.
%28x-1%29%28x-2%29+=+0 Apply the zero product rule.
x-1+=+0 or x-2+=+0 so...
x+=+1 or x+=+2
However, notice that when you substitute x = 1 into the given equation, you will get undefined terms:
%28x%2F2%29%2B%281%2F%28x-1%29%29+=+x%2F%28x-1%29 Substitute x = 1.
%281%2F2%29%2B%281%2F%281-1%29%29+=+1%2F%281-1%29 or...
%281%2F2%29%2B1%2F0+=+1%2F0 but 1%2F0 is undefined, so x = 1 is an excluded solution.
Answer: highlight%28x+=+2%29