Simplify: a/1-{1/[1+(1/a-1)]}

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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`a/(1-{1/[1+(1/a-1)]})`

We will remove the inside out.

First we will simplify inside the paranthesis ( ).

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

==> `a/(1-{1/[1+ (1-a)/a]})`

Now we will simplify between [ ] .

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

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

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

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