Problem

A curve $C$ has parametric equations

$$x=\frac{t}{t-3}\qquad y=\frac{1}{t}+2\qquad t\in\mathbb{R}\qquad t>3$$

Show that all points on $C$ lie on the curve with Cartesian equation

$$y=\frac{ax-1}{bx}$$

where $a$ and $b$ are constants to be found.