So here's my problem:

Find where the given function is increasing and decreasing.

$\displaystyle f(x)=\frac{x-1}{x^2}$

So $\displaystyle f'(x)=\frac{(x-1)(2x)-(x^2)(1)}{(x^2)^2)}$

$\displaystyle =\frac{2x^2-2x-x^2}{(x^2)^2)}$

$\displaystyle =\frac{x^2-2x}{(x^2)^2}$

So to find the split points would I solve $\displaystyle 2x^2-2x>0$ and $\displaystyle 2x^2-2x<0$ ?