Find the set on which h is continuous.
h(x,y)=(5-xy)/(2+x^2 y^2) +ln((5-xy)/(2+x^2 y^2))
h will be continuous where
no denominator is zero, and ln is defined
(2 + x^2y^2) is always positive, so that is no problem
ln is defined where 5-xy > 0
So, h(x,y) is continuous everywhere except where xy > 5