# How do you find the derivative of y = (x+2)/(x-2) ?

Using the quotient rule, which states that for $y = f \frac{x}{g} \left(x\right)$, we'll have $y ' = \frac{f ' \left(x\right) g \left(x\right) - f \left(x\right) g ' \left(x\right)}{g {\left(x\right)}^{2}}$, we have
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1 \cdot \left(x - 2\right) - \left(x + 2\right) \cdot 1}{x - 2} ^ 2 = \frac{\cancel{x} - 2 - \cancel{x} - 2}{x - 2} ^ 2 = - \frac{4}{x - 2} ^ 2$