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

$f = {\left(x + 3\right)}^{2} , g = x - 1 \to f ' = 2 \left(x + 3\right) \cdot 1 = 2 x + 6 , g ' = 1 \to y ' = \left(\frac{g f ' - f g '}{g} ^ 2\right) = \frac{\left(x - 1\right) \left(2 x + 6\right) - {\left(x + 3\right)}^{2}}{x - 1} ^ 2 = \frac{2 {x}^{2} + 4 x - 6 - {x}^{2} - 6 x - 9}{x - 1} ^ 2 = \frac{{x}^{2} - 2 x - 15}{x - 1} ^ 2$