Find the inverse of the function given: $$f(x)= \frac{5x}{(x − 2)}$$
My work:
$$y=\frac{5x}{(x-2)}$$
$$x=\frac{5y}{(y-2)}$$
$$x(y-2)=5y$$
$$xy-2x=5y$$
$$\frac{xy-2x}{5}=y$$
$$f(x)=\frac{(xy-2x)}{5}$$
Any help is appreciated.

Solve for $x$ in $y=\frac{5x}{x-2}$:
$$
y(x-2)=5x\\
\Downarrow\\
yx-5x=2y\\
\Downarrow\\
x(y-5)=2y\\
\Downarrow\\
x=\frac{2y}{y-5}
$$
This implies the inverse is $f(x)=\frac{2x}{x-5}$.
