Help differentiating $\frac{(x-1)^2(x+2)^2}{(x+1)^2}$ I need help differentiating this expression below. I know you can use a mix of the product rule and quotient rule, but that is tedious and long. Is there a shorter method?
$$\dfrac{(x-1)^2(x+2)^2}{(x+1)^2}$$

Use this way for a short-cut :
Let :
$$f(x) = \dfrac{(x-1)^2(x+2)^2}{(x+1)^2}$$
$$\ln {f(x)} = \ln (x-1)^2 +\ln(x+2)^2-\ln(x+1)^2 $$ 
$$\dfrac{f'(x)}{f(x)} = \frac{2(x-1)}{(x-1)^2}+\frac{2(x+2)}{(x+2)^2}-\frac{2(x+1)}{(x+1)^2} $$
$$f'(x) =  \dfrac{(x-1)^2(x+2)^2}{(x+1)^2} \Bigg(\frac{2}{(x-1)}+\frac{2}{(x+2)}-\frac{2}{(x+1)} \Bigg)$$
