## Intermediate Algebra for College Students (7th Edition)

$\displaystyle \frac{x+5}{x^{3}-1}\quad$or$\displaystyle \quad\frac{x+5}{(x-1)(x^{2}+x+1)}$
$x^{3}-1$ is a difference of cubes, $x^{3}-1^{3}=(x-1)(x^{2}+x+1)$ $x^{2}+x+1$ has no real zeros as $b^{2}-4ac=1-4$ ... is negative. LCD = $(x-1)(x^{2}+x+1)=x^{3}-1$ Write all fractions with the LCD, $\displaystyle \frac{2}{x^{3}-1}+\frac{4}{x^{3}-1}+\frac{1}{x^{2}+x+1}\cdot\frac{x-1}{x-1}=$ $=\displaystyle \frac{2+4+x-1}{x^{3}-1}$ $=\displaystyle \frac{x+5}{x^{3}-1}\quad$or$\displaystyle \quad\frac{x+5}{(x-1)(x^{2}+x+1)}$