Answer
The domain $D$ consists of all points $\left( {x,t} \right)$ not lying on the line $t = - x$:
$D = \left\{ {\left( {x,t} \right)|t \ne - x} \right\}$
Work Step by Step
The function $h\left( {x,t} \right) = \frac{1}{{x + t}}$ is defined only when $t \ne - x$. Thus, the domain $D$ consists of all points $\left( {x,t} \right)$ not lying on the line $t = - x$:
$D = \left\{ {\left( {x,t} \right)|t \ne - x} \right\}$
