Question
Prove that:
$(\text{a}^{-1}+\text{b}^{-1})=\frac{\text{ab}}{\text{a}+\text{b}}$
$(\text{a}^{-1}+\text{b}^{-1})=\frac{\text{ab}}{\text{a}+\text{b}}$
✓
Answer
$\text{LHS}=(\text{a}^{-1}+\text{b}^{-1})$
$=\Big(\frac{1}{\text{a}}+\frac{1}{\text{b}}\Big)^{-1}$
$=\Big(\frac{\text{b}+\text{a}}{\text{ab}}\Big)^{-1}$
$=\frac{\text{ab}}{\text{a}+\text{b}}$
$=\text{RHS}$
Therefore, $LHS = RHS$ Hence proved
$=\Big(\frac{1}{\text{a}}+\frac{1}{\text{b}}\Big)^{-1}$
$=\Big(\frac{\text{b}+\text{a}}{\text{ab}}\Big)^{-1}$
$=\frac{\text{ab}}{\text{a}+\text{b}}$
$=\text{RHS}$
Therefore, $LHS = RHS$ Hence proved
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