Did i simpifly this correctly? How can I simplify $$\frac{\frac{1}{x+h-1} - \frac{1}{x-1}}{h} \ \ ? $$  
I can't figure out how to do it correctly on the website. 
I got $\frac{1}{(h+x-1)(x-1)}$

It is almost right. You have forgotten the negative sign.
$$\lim_{h\to 0}-\frac{1}{(h+x-1)(x-1)}=\lim_{h\to 0}-\frac{1}{h(x-1)+x(x-1)-(x-1)}=-\frac{1}{x(x-1)-(x-1)}$$
$$=-\frac1{x^2-x-x+1}=-\frac{1}{(x-1)^2}$$
This is the derivative of $\frac{1}{x-1}$.
