Question

Write the following in the simplest form:
(b^-2 - a^-2) ÷ (b^-1 - a^-1)

Answer 1

(b^-2 - a^-2) ÷ (b^-1 - a^-1)

This can be written as,

= `(1/b^2 - 1/a^2)/(1/b - 1/a)`

= `{(1/b)^2 - (1/a)^2}/(1/b - 1/a)`

= `= {(1/b + 1/a) (1/b - 1/a)}/(1/b — 1/a)`

We get,

= `1/b + 1/a`