$\text{ The line }\mathrm{x}+\mathrm{y}+1=0\text{ is an asymptote of }{\mathrm{x}}^2-{\mathrm{y}}^2+\mathrm{x}-\mathrm{y}-2=0\text{. The other asymptote is }$

$$\begin{gathered} Given hyperbola x^2-y^2+x-y-2=0 \\ This is rec\tan gular hyperbola \\ centre =(\frac{-1}{2},\frac{-1}{2}) \\ Given one asymptote is x+y+1=0 \end{gathered}$$

since for rectangular hyperbola asymptotes are perpendicular then

$$\begin{gathered} \mathrm{Other} \mathrm{asymptote} \mathrm{of} \mathrm{rectangular} \mathrm{hyperbola} \mathrm{is} \mathrm{x}-\mathrm{y}=\mathrm{k} \\ \mathrm{It} \mathrm{passes} \mathrm{through} \mathrm{the} \mathrm{poinyt} (\frac{-1}{2},\frac{-1}{2}) \\ \mathrm{then} \mathrm{k}=0 \\ \mathrm{so} \mathrm{required} \mathrm{asymptote} \mathrm{is} \mathrm{x}-\mathrm{y}=0 \end{gathered}$$