Question

How do you divide `(2x^2-6x+6)/(2x - 3)`?

Answer 1

`x-3-3/(2x-3)`

Explanation:

`(2x^2-6x+6)-:(2x-3)`

color(magenta)(
color(white)(
`" "2x^2-6x+6`
`color(magenta)(x)(2x-3) ->" "ul(2x^2-3x" ")larr" Subtract"`
`" "0color(white)(.)-6x+6`
`color(magenta)(-3)(2x-3)->" "ul(-6x+9)larr" Subtract"`
`" "0color(white)(.)color(magenta)(-3)larr" Remainder"`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(magenta)(x-3-) (color(magenta)(3))/(2x-3)`