$$( u ^ { 2 } - 2 ) g ( t ) = \sqrt { t ^ { 2 } + t + t + 4 }$$
$g=\frac{\sqrt{t^{2}+2t+4}}{t\left(u^{2}-2\right)}$
$t\neq 0\text{ and }|u|\neq \sqrt{2}$
