For x close to 1, e^y(x-1)≈1+y(x-1) so
This shows x=1 is a removable discontinuity in
the neighborhood of (1,2). So we can cancel the
factors (x-1) and define the function to be -y/(y+1)
when x=1 with y near 2.
Therefore lim -y/(y+1) when (x,y)-->(1,2) is -2/3.