What is 1/(1-\frac{1){1-1/(a+1)}} ?

The solution to 1/(1-\frac{1){1-1/(a+1)}} is -a

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simplify 1/(1-\frac{1){1-1/(a+1)}}

simplify

\frac{1}{1 - \frac{1}{1 - \frac{1}{a + 1}}}

- a

Solution steps

\frac{1}{1 - \frac{1}{1 - \frac{1}{a + 1}}}

\frac{1}{1 - \frac{1}{a + 1}} = \frac{a + 1}{a}

= \frac{1}{1 - \frac{a + 1}{a}}

Join

1 - \frac{a + 1}{a} : - \frac{1}{a}

= \frac{1}{- \frac{1}{a}}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{1}{\frac{1}{a}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

\frac{1}{\frac{1}{a}} = \frac{a}{1}

= - \frac{a}{1}

Apply rule

\frac{a}{1} = a

= - a

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What is 1/(1-\frac{1){1-1/(a+1)}} ?
The solution to 1/(1-\frac{1){1-1/(a+1)}} is -a