Simplify :

(a^-1 + b^-1) ÷ (ab)^-1

Given,

(a^-1 + b^-1) ÷ (ab)^-1

Simplifying the expression :

$\Rightarrow \Big(\dfrac{1}{a} + \dfrac{1}{b}\Big) ÷ \Big(\dfrac{1}{ab}\Big) \\[1em] \Rightarrow \Big(\dfrac{b + a}{ab}\Big) ÷ \Big(\dfrac{1}{ab}\Big) \\[1em] \Rightarrow \Big(\dfrac{a + b}{ab}\Big) \times ab \\[1em] \Rightarrow a + b.$

Hence, $(a^{-1} + b^{-1}) ÷ (ab)^{-1} = (a + b)$.