Question
Simplify $:(a+b)^{-1} \cdot\left(a^{-1}+b^{-1}\right)$
✓
Answer
$ (a+b)^{-1} \cdot\left(a^{-1}+b^{-1}\right)$
$ =\frac{1}{a+b} \times\left(\frac{1}{a}+\frac{1}{b}\right)$
$ =\frac{1}{a+b} \times\left(\frac{b+a}{a b}\right)$
$ =\frac{1}{a+b} \times \frac{a+b}{a b}$
$ =\frac{1}{a b}$
$ =\frac{1}{a+b} \times\left(\frac{1}{a}+\frac{1}{b}\right)$
$ =\frac{1}{a+b} \times\left(\frac{b+a}{a b}\right)$
$ =\frac{1}{a+b} \times \frac{a+b}{a b}$
$ =\frac{1}{a b}$
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