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

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

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simplify 1/((1-\frac{1){(1-1/y)})}

simplify

\frac{1}{( 1 - \frac{1}{( 1 - \frac{1}{y} )} )}

- y + 1

Solution steps

\frac{1}{1 - \frac{1}{1 - \frac{1}{y}}}

\frac{1}{1 - \frac{1}{y}} = \frac{y}{y - 1}

= \frac{1}{1 - \frac{y}{y - 1}}

Join

1 - \frac{y}{y - 1} : - \frac{1}{y - 1}

= \frac{1}{- \frac{1}{y - 1}}

Apply the fraction rule:

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

= - \frac{1}{\frac{1}{y - 1}}

Apply the fraction rule:

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

\frac{1}{\frac{1}{y - 1}} = \frac{y - 1}{1}

= - \frac{y - 1}{1}

Apply rule

\frac{a}{1} = a

= - (y - 1)

Distribute parentheses

= - (y) - (- 1)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - y + 1

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