not too sure how to do limits in multivariable yet.

heres my question?:

Limit as (x,y)-->(0,0) of (e^(xy)-1)/y.

I know the answer is zero from the back of the book but how i did it it got negative infinite.

I multiplied by x/x so the function was (xe^(xy)-x)/(xy) and split it into two limits. The first limit (xe^(xy))/xy goes to 0 i think, and then -x/(xy) i think goes to - infinity.

how do i actually do this/whats wrong with what i did?