# How do you divide (x^2+7x+15)/(x-5)?

Jul 11, 2016

$\frac{{x}^{2} + 7 x + 15}{x - 5} = x + 12 + \frac{75}{x - 5}$

#### Explanation:

EDIT: The formatting is screwed up for some reason, it looks fine in preview. Not really sure how to deal with it :/

$\text{ } {x}^{2} + 7 x + 15$
color(blue)(x)(x-5)->color(white)(....)ul(x^2-5x)"
$\text{ } 0 \textcolor{w h i t e}{.} + 12 x + 15$
$\textcolor{b l u e}{12} \left(x - 5\right) \to \text{ "color(white)(.)ul(12x-60)}$
" "color(red)("0+75 " larr " Remainder")

The parts in blue denote the result from dividing in at each point, while the red deals with remainder. Combining these gives:

$\frac{{x}^{2} + 7 x + 15}{x - 5} = \textcolor{b l u e}{x + 12} + \frac{\textcolor{red}{75}}{x - 5}$