<s>[INST] Help with this multi variable limit. $ \lim_{x,y\to (1,0)}  \frac{2x^4+x^2y^2-2x^2-y^2}{2x^2y^2-x^2-2y^2+1} $
By just plugging in $(1,0)$ into the limit you get $-2$, but I don't know if this enough to solve the question 
Ive tried approaching along $x=y+1$ but it got extremely messy.
 [/INST] You have 
$$
 \frac{2x^4+x^2y^2-2x^2-y^2}{2x^2y^2-x^2-2y^2+1}= \frac{(2x^2+y^2)(x^2-1)}{(2y^2-1)(x^2-1)}= \frac{2x^2+y^2}{2y^2-1}\to\frac2{-1}
$$
</s>