Question

(a-¹ + b-¹) ÷( a-² - b-²)

Answer 1

$\frac{a ^{ - 1} + {b}^{ - 1} }{ {a}^{ - 2} - {b}^{ - 2} }$
$= \frac{( {a}^{ - 1} + {b}^{ - 1} )}{( {a}^{ - 1} + {b}^{ - 1} )( {a}^{ - 1} - {b}^{ - 1} )}$
$= \frac{1}{( {a}^{ - 1} - {b}^{ - 1} )}$
$= \frac{1}{ \frac{1}{a} - \frac{1}{b} }$
$= \frac{1}{ \frac{b - a}{ab} }$
$= \frac{ab}{b - a}$

Answer 2

I hope that this might be of any help :)