# How do you differentiate e^x/(x-1) using the quotient rule?

Quotient rule states that for a function $y = f \frac{x}{g} \left(x\right)$, then $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{f ' \left(x\right) g \left(x\right) - f \left(x\right) g ' \left(x\right)}{g} {\left(x\right)}^{2}$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{{e}^{x} \left(x - 1\right) - {e}^{x} \left(1\right)}{x - 1} ^ 2$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{{e}^{x} \left(x - 2\right)}{x - 1} ^ 2$