Lim x^2-4y^2/(x+2y) as (x,y)->(-2,1): -4 or DNE?

[Dustinsfl]

lim (x^2-4y^2)/(x+2y) as (x,y)->(-2,1)
Does this limit go to -4 or DNE since it is undefined all along x+2y?

 

[HallsofIvy]

It Does Not Exist.

 

[arildno]

Please note that you may write this as:
$$\frac{x^{2}-4y^{2}}{x+2y}=\frac{(x-2y)(x+2y)}{x+2y}=x-2y,x\neq{-}2y$$