What is the reciprocal of $\frac {x}{y} - 1?$ Isn’t it $\frac {y}{(x - y)}?$ But I don’t see this answer in the multiple choice.
$\frac {x}{y} - 1$ = $\frac {x - y}{y}$ and reciprocal is $\frac {y}{x - y}$.
Edited: My apologies for not providing complete question. The question is as below:
"Which of the following equals the reciprocal of $\frac {x}{y} - 1$, where $\frac {x}{y} - 1$ does not equal to 0?"
The choices of the answers are (A) $\frac {1}{x} - y$, (B) -$\frac {y}{x}$, (C) $\frac{y}{x-1}$, (D) $\frac{x}{xy-1}$ and (E) $\frac{y}{xy-1}$.
Yes you are correct. Given that $\frac{x}{y}-1 = \frac{x-y}{y}$, then the reciprocal is $\frac{y}{x-y}$.
If this answer is not one of the options, maybe realise that this fraction is equal to $1- \frac{x}{x-y}$.