How do you simplify ${(a^{- 1} + b^{- 1})}^{- 1}$ $(a^-1 + b^-1)^-1$ ?

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Answer 1 · 2016-01-10T20:48:42

$\frac{a b}{a + b}$ $(ab)/(a+b)$

The power of -1 means find the reciprocal (i.e. 1 divided by the value)

Write $a^{- 1}$ $a^-1$ as $\frac{1}{a}$ $1/a$ and $b^{- 1}$ $b^-1$ as $\frac{1}{b}$ $1/b$

Then:
${(\frac{1}{a} + \frac{1}{b})}^{- 1} = {(\frac{a + b}{a b})}^{- 1} = \frac{a b}{a + b}$ $(1/a+1/b)^-1 = ((a+b)/(ab))^-1 = (ab)/(a+b)$

How do you simplify (a−1+b−1)−1(a^-1 + b^-1)^-1?