Answer
Domain: $D=$ {$(x,y) | x^2+y^2 \neq 1$}
Work Step by Step
We are given that $f(x,y)=\dfrac{(1+x^2+y^2)}{(1-x^2-y^2)}$
The function $f(x,y)=\dfrac{(1+x^2+y^2)}{(1-x^2-y^2)}$
represents a rational function which is continuous on its domain $D$. The function is defined when the denominator is not zero.
Thus,
$ 1-x^2-y^2 \neq 0$
or, $x^2+y^2 \neq 1$
Hence, Domain: $D=$ {$(x,y) | x^2+y^2 \neq 1$}
