SOLUTION: I need to solve this (1/x-1)-(1/x)=1/6x I need help finding the LCD

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Question 435286: I need to solve this
(1/x-1)-(1/x)=1/6x
I need help finding the LCD
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
I assume the RHS is 1/(6x) and not (1/6)x. If so, then we solve in the following way:
1%2F%28x-1%29+-+1%2Fx+=+1%2F6x
To obtain a common denominator multiply the two terms together, which gives:
%28x+-+%28x-1%29%29%2F%28x%28x-1%29%29+=+1%2F6x
Collect terms in the numerator:
1%2F%28x%28x%2B1%29%29+=+1%2F6x
Cross-multiply and solve for x:
x%28x-1%29+=+6x+-%3E+x-1+=+6+-%3E+x+=+7
Check:
1/6 - 1/7 = 1/42
7/42 - 6/42 = 1/42