I was reading this paper. I didn't understand something on the 5th page:
"We may suppose that $a\geq b>0$. If $b\geq 5$ then $\frac{2a+2b-4}{ab-4}\leq \frac{2a+2b-4}{5b-4}<1$."
Why? $\frac{2a+2b-4}{5b-4}<1$ is only possible when $2a<3b$ but I can't see any way to deduce that.
I'd say that it is a typo. It should be $$\frac{2a+2b-4}{ab-4}\le\frac{2a+2b-4}{5a-4}<1$$