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Solving a Quadratic Equation by Completion of Squares Method

Prove that: ...

Question

Prove that:
$(a^{- 1} + b^{- 1})^{- 1} = \frac{a b}{a + b}$

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Solution

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

So, $(a^{- 1} + b^{- 1})^{- 1} = \frac{a b}{a + b}$

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Prove that

(a^-1 + b^-1)^-1 = ab/a+b

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then prove that

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