Write the equation in this form : $(a-b)^2 = 3(ab-1)(ab+2a+2b+3)$

Now you can easily prove that except only finitely cases we have $3|ab+2a+2b+3| > |a-b|$ and $|ab-1| > |a-b| $

For example, $(ab-1)^2 \geq (a-b)^2 $ if $(a^2 - 1)(b^2 -1) \geq 0$