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Popular >

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

Solution

simplify

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

Solution

b + a

Solution steps

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

Join

\frac{b}{a} - \frac{a}{b} : \frac{b ^{2} - a ^{2}}{ba}

= \frac{\frac{b ^{2} - a ^{2}}{ba}}{\frac{1}{a} - \frac{1}{b}}

Join

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

= \frac{\frac{b ^{2} - a ^{2}}{ba}}{\frac{b - a}{ba}}

Apply the fraction rule:

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

= \frac{( b ^{2} - a ^{2} ) ba}{ba ( b - a )}

Cancel

\frac{( b ^{2} - a ^{2} ) ba}{ba ( b - a )} : b + a

= b + a

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Frequently Asked Questions (FAQ)

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