Chapter 12 - Functions of Several Veriables - 12.2 Graphs and Level Curves - 12.2 Exercises - Page 882: 16

$$D = \left\{ {\left( {x,y} \right):x \ne y} \right\}$$

$$\eqalign{ & f\left( {x,y} \right) = \frac{{12}}{{{y^2} - {x^2}}} \cr & {\text{The denominator of the function cannot be 0, the function}} \cr & {\text{is not definef for }}{y^2} - {x^2} \ne 0. \cr & {y^2} \ne {x^2} \cr & x \ne y \cr & {\text{Therefore, the domain of }}f{\text{ is }}D = \left\{ {\left( {x,y} \right):x \ne y} \right\} \cr} $$