# How do you derive y = (x-1)/( x+3) ^ (2) using the quotient rule?

$\frac{d}{\mathrm{dx}} \left(\frac{x - 1}{x + 3} ^ 2\right) = \frac{{\left(x + 3\right)}^{2} - 2 \left(x - 1\right) \left(x + 3\right)}{x + 3} ^ 4$
The quotient rule states that $\frac{d}{\mathrm{dx}} \left(\frac{f \left(x\right)}{g \left(x\right)}\right) = \frac{g \left(x\right) \cdot f ' \left(x\right) - f \left(x\right) \cdot g ' \left(x\right)}{g \left(x\right)} ^ 2$
$\frac{d}{\mathrm{dx}} \left(\frac{x - 1}{x + 3} ^ 2\right) = \frac{{\left(x + 3\right)}^{2} \cdot \left(1\right) - \left(x - 1\right) \cdot 2 \left(x + 3\right)}{x + 3} ^ 4$