What is (a+b)/(a^{-1)+b^{-1}} ?

The solution to (a+b)/(a^{-1)+b^{-1}} is ab

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simplify (a+b)/(a^{-1)+b^{-1}}

simplify

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

ab

Solution steps

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

Simplify

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

= \frac{a + b}{\frac{b + a}{ab}}

Apply the fraction rule:

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

= \frac{( a + b ) ab}{b + a}

Cancel

\frac{( a + b ) ab}{b + a} : ab

= ab

\frac{3}{28}

(7 + 5 i)^{2}

62 + 58 + 232

\frac{53}{8}

\frac{53}{5}