Simplify: `a/1-(1/(1+(1/(a-1))))`

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justaguide eNotes educator| Certified Educator

The expression `a/1-(1/(1+(1/(a-1))))` has to be simplified.

`a/1-(1/(1+(1/(a-1))))`

=> `a/1-(1/((a - 1+1)/(a-1)))`

=> `a/1-(1/(a/(a-1)))`

=> `a/1-((a - 1)/a)`

=> `(a^2 - a + 1)/a`

The expression `a/1-(1/(1+(1/(a-1))))` can be simplified as `(a^2 - a + 1)/a`

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