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$\begingroup$ How do I simplify the expression ...
$$(a^{-1} + b^{-1}) ^{-1}$$ ?
$\endgroup$ 1 1 Answer
$\begingroup$ If you have meant $$\left(a^{-1}+b^{-1}\right)^{-1}$$
it is equal to $$\frac1{a^{-1}+b^{-1}}=\frac1{\frac1a+\frac1b}=\frac{ab}{b+a}$$ multiplying the numerator & the denominator by $ab$
assuming $a,b$ to be non-zero numbers
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