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Question 396761: Please help me solve this equation.

Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
1+-+1%2F%281-+1%2F%281+-+1%2Fx%29%29+=+8
Although one can do this by repeatedly subtracting the fractions, I like to do these differently. Working from the bottom we can multiply the numerator and denominator of a "big" fraction by the lowest common denominator (LCD) of the "little" fraction(s).

Fisrt we work with the 1%2F%281+-+1%2Fx%29 fraction at the bottom. The LCD is just "x" (since there is just the one "little" fraction in this "big" fraction. So we multiply the numerator and denominator of this "big" fraction by x:
1+-+1%2F%281-+%281%2F%281+-+1%2Fx%29%29%2A%28x%2Fx%29%29+=+8
giving us:
1+-+1%2F%281-+x%2F%28x+-+1%29%29+=+8
Now we'll work with the 1%2F%281-x%2F%28x-1%29%29 fraction. The LCD here is (x-1) so we multiply the numerator and denominator by (x-1):
1+-+%281%2F%281-+x%2F%28x+-+1%29%29%29%28%28x-1%29%2F%28x-1%29%29+=+8
giving us:
1+-+%28x-1%29%2F%28%28x-1%29-x%29+=+8
which simplifies as follows:
1+-+%28x-1%29%2F%28-1%29+=+8
1+%2B+%28x-1%29%2F%281%29+=+8
1 + (x-1) = 8
x = 8