<s>[INST] If $\frac{a}{b}=\frac{x}{y}$, is $\frac{x-a}{y-b}=\frac{x}{y}$? Does this hold?  $b,y \neq 0$, $b \neq y$.
 [/INST] \begin{align}
\frac{a}{b}&=\frac{x}{y}\\
\frac{x}{a}&=\frac{y}{b}\\
\frac{x}{a}-1&=\frac{y}{b}-1\\
\frac{x-a}{a}&=\frac{y-b}{b}\\
\frac{x-a}{y-b}&=\frac{a}{b}\\
\frac{x-a}{y-b}&=\frac{x}{y}
\end{align}
</s>