Answer
$\frac{u^{2}+3u+1}{u+1}$
Work Step by Step
$u+1+\frac{u}{u+1}$
Convert all elements to a fraction:
$=\frac{u}{1}+\frac{1}{1}+\frac{u}{u+1}$
Find the lowest common denominator (i.e. $u+1$) and adjust the fractions accordingly:
$=\frac{u\times (u+1)}{1\times (u+1)}+\frac{1\times (u+1)}{1\times (u+1)}+\frac{u}{u+1}$
Expand any brackets:
$=\frac{u^{2}+u}{u+1}+\frac{u+1}{u+1}+\frac{u}{u+1}$
Combine fractions:
$=\frac{u^{2}+u+u+1+u}{u+1}$
Collect the like terms:
$=\frac{u^{2}+3u+1}{u+1}$
