# How do you differentiate the following parametric equation:  x(t)=t/(t-4), y(t)=1+t ?

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{dt}} \cdot \frac{\mathrm{dt}}{\mathrm{dx}}$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{dt}} / \frac{\mathrm{dx}}{\mathrm{dt}}$
$\frac{\mathrm{dx}}{\mathrm{dt}} = \frac{t - 4 - t}{t - 4} ^ 2 = - \frac{4}{t - 4} ^ 2$
$\frac{\mathrm{dy}}{\mathrm{dt}} = 1$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{- \frac{4}{t - 4} ^ 2} = - {\left(t - 4\right)}^{2} / 4$