Solving a Parametric Position Equation

A particle moves along a path with positions given by
$x(t)=\frac{t^2+4*t+4}{t+2}$ and
$y(t)=\sqrt{\frac{9*t^2+12*t+4}{t^2+4*t+4}}.$
Find the value of $t$ for which $x(t)+y(t)=8.$