Prove that $\lim\limits_{(x,y) \to (0,0)} \frac{3x^{2}y}{x^{4}-2x^{2}y + 5y^{2}}$ does not exist Wolframalpha says that
$$\lim\limits_{(x,y) \to (0,0)} \frac{3x^{2}y}{x^{4}-2x^{2}y + 5y^{2}}$$
does not exist.
But I can not find a way to prove it, using $\gamma1(t) = (0,t)$, $\gamma(t) = (t,0)$ and $\gamma(t) = (t,t)$ gives me zero.
Can anyone please, help me?

$(x,y)=(t,t^2)$ gives $\frac{3x^2y}{x^4-2x^2y+5y^2}=\frac{3t^4}{t^4-2t^4+5t^4}=\frac{3t^4}{4t^4}=\frac{3}{4}$ so the limit is $\frac{3}{4}$ along this path to the origin while $(x,y)=(t,t)$ gives $\frac{3x^2y}{x^4-2x^2y+5y^2}=\frac{3t^3}{4t^4}=\frac{3t^3}{t^4-2t^3+5t^2}=\frac{3t}{t^2-2t+5}$ so the limit is $0$ along this other path to the origin.
