Question

Find the quotient when $(x^{-1}-1)$ is divided by $(x-1)$

• A. $-\frac{1}{x}$
• B. $-\frac{2}{x}$
• C. $-\frac{1}{x^2}$
• D. $-\frac{2}{x^2}$

Answer 1

The correct option is A $-\frac{1}{x}$

Quotient $=\frac{x^{-1}-1}{x-1}$
$=\frac{(\frac{1}{x}-1)}{x-1}$

$=\frac{1-x}{x}\times \frac{1}{x-1}$

$=-\frac{1}{x}$