Question

Simplify the following

`( (1)/(a) - (1)/(b)) {}^( - 1)`
​

Answer 1

Explanation:

`(1)/(a)-(1)/(b) =(1*b)/(a*b)-(1*a)/(b*a)\\\\=(b)/(ab)-(a)/(ab)\\\\=(b-a)/(ab)\\\\\\((1)/(a)-(1)/(b))^(-1) = ((b-a)/(ab))*{-1}\\\\=(ab)/(b-a)`