Multivariable limit problem

If

$\displaystyle

limit

(x,y,z) -> (1,-1,1) for

(xy + yz + zx)/(1 + xyz)$

When I plug in values, I get -1/0 which is undefined. My question is, how do I prove that the limit does not exist? I can't set y=mx because y and x do not necessarily follow the same path to the point (1,-1,1) and using polar coordinate substitution does not seem to work here. I tried setting z=x but that still gives me a 0 in the denominator because of the -1 for the y. Finally, multiplying the equation by various values of 1 (such as multiplying y squared to both the numerator and denominator) don't solve the undefined issue.