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Popular >

simplify (a-1/b)/(b-1/a)

Solution

simplify

\frac{a - \frac{1}{b}}{b - \frac{1}{a}}

Solution

\frac{a}{b}

Solution steps

\frac{a - \frac{1}{b}}{b - \frac{1}{a}}

Join

a - \frac{1}{b} : \frac{ab - 1}{b}

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

Join

b - \frac{1}{a} : \frac{ba - 1}{a}

= \frac{\frac{ab - 1}{b}}{\frac{ba - 1}{a}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( ab - 1 ) a}{b ( ba - 1 )}

Cancel

\frac{( ab - 1 ) a}{b ( ba - 1 )} : \frac{a}{b}

= \frac{a}{b}

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Frequently Asked Questions (FAQ)

What is (a-1/b)/(b-1/a) ?
The solution to (a-1/b)/(b-1/a) is a/b