I've been stuck on this problem for a few days and was hoping somebody could point me in the right direction.

$\displaystyle lim{yto4}\frac{\frac{1}{y}}{y-4}-\frac{\frac{1}{4}}{y-4}$

I try to flip the denominator (y-4) and multiply across $\displaystyle \frac{1}{y}*{\frac{1}{y-4}-\frac{1}{4}*{\frac{1}{y-4}$ which yields $\displaystyle \frac{1}{y^2-4y}-\frac{1}{4y-16}$

And then I multiply one side by 4/4 and the other by y/y which gives $\displaystyle \frac{4}{4y^2-16y}-\frac{y}{4y^2-16y}$ ... When I go to evaluate the limit here I get 0/0 which I already know is incorrect. Even if I simplify the 4's further I get a wrong answer, and I guess at this point I'm just not sure if I'm going in the right direction.

Sorry about the LaTeX being a little sloppy, I kind of typed this in a hurry before class. The top should be "lim as y approaches 4"