Question

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

Answer 1

`(x^2+7x+15)/(x-5) = x + 12 + 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 :/

`" "x^2+7x+15`
`color(blue)(x)(x-5)->color(white)(....)ul(x^2-5x)"`
`" "0color(white)(.)+12x+15`
`color(blue)(12)(x-5)->" "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:

`(x^2+7x+15)/(x-5) = color(blue)(x + 12) + (color(red)(75))/(x-5)`