I need to find:

lim as (x,y) => (0,0) of ((x - y)^2) / (abs(x) + abs(y))

I know that the limit should be 0, and I am searching for a bounding function B(x) to use the squeeze theorem with.

I have so far:

0 <= abs[f(x,y) - L] = abs[((x - y)^2) / (abs(x) + abs(y))]

<= ((x - y)^2) / abs(x + y)

dropping the absolute value bars since all terms are positive, and combining abs(x) and abs(y) using the triangle inequality

Where can I go from here to remove the denominator and find a bounding function?