## Thomas' Calculus 13th Edition

$\dfrac{1}{2}$
$\lim\limits_{(x,y) \to (2,-4)} \dfrac{(y+4)}{x(xy-y+4x-4)}=\lim\limits_{(x,y) \to (2,-4)} \dfrac{(y+4)}{x(x-1)(y+4)}=\dfrac{1}{2(2-1)}$ Plug the limits, then we get $\dfrac{1}{2(1)}=\dfrac{1}{2}$