## Precalculus: Mathematics for Calculus, 7th Edition

$\frac{2x+1}{x^{2}(x+1)}$
$\frac{1}{x^{2}}+\frac{1}{x^{2}+x}$ Factor out the common term from the second fraction: $=\frac{1}{x^{2}}+\frac{1}{x(x+1)}$ Find the least common denominator (i.e. $x^{2}(x+1)$) and adjust the fractions accordingly: $=\frac{1\times (x+1)}{x^{2}(x+1)}+\frac{1\times x}{x^{2}(x+1)}$ Simplify the fractions: $=\frac{x+1}{x^{2}(x+1)}+\frac{x}{x^{2}(x+1)}$ Combine the fractions: $=\frac{x+1+x}{x^{2}(x+1)}$ Collect the like terms: $=\frac{2x+1}{x^{2}(x+1)}$