Answer
all real $u$, $u\ne-1,-2$
Work Step by Step
$\because$ the denominator of $\frac{1}{u+1}\ne0,$
$u+1\ne0, u\ne-1$
$f(u)=\frac{(u+1)(u+1)}{(u+1)+1}
=\frac{u^{2}+2u+1}{u+2}$
$\because$ the denominator of $f(u)\ne0$,
$u+2\ne0, u\ne-2$
$\therefore$ the domain is all real $u$, excluding $u=-1,-2$
