## Precalculus: Mathematics for Calculus, 7th Edition

$\frac{u^{2}+3u+1}{u+1}$
$u+1+\frac{u}{u+1}$ 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: $=\frac{u^{2}+3u+1}{u+1}$