Question 97261
 (x/(x-2)) - ((x+1)/x) = 8/(x^2-2x)

Multiply thru by x(x-2) to get rid of the denominators:

x*x - (x+1)(x-2) = 8

x^2 - [x^2-x-2] = 8
x+2 = 8
x = 6
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Checking:
6/(4) - 7/6 =  8/(36-12)
3/2 - 7/6 = 8/24
9/6 - 7/6 = 2/6
2/6 = 2/6
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Cheers,
Stan H.