Question

How do you solve for the quotient of (x^-1) - 1 ÷ x - 1?

Answer 1

`\bf x^(-1)-1/ x-1\implies \implies \cfrac{1}{x}-1/ x-1\implies \cfrac{(1)/(x)-1}{~~x-1~~}\implies \cfrac{~~(1-x)/(x)~~}{(x-1)/(1)} \\\\\\ \cfrac{1-x}{x}\cdot \cfrac{1}{x-1}\implies \cfrac{-(\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix})}{x}\cdot \cfrac{1}{\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies -\cfrac{1}{x}\implies -x^(-1)`