Question

How do you divide `(x-2)^2/(x^2-5x+9)`?

Answer 1

`(x^2-4x+4)/(x^2-5x+9)" "=" " 1 +(x-5)/(x^2-5x+9)`

Explanation:

Look at https://socratic.org/s/avjGBRiF as a further example of the method.

Write as `(color(blue)(x^2-4x+4))/(color(green)(x^2-5x+9))`

`"Numerator "->" "color(blue)( x^2-4x+4)`
`color(magenta)(1xx)color(green)((x^2-5x+9)) ->" "ul(x^2-5x+9)" "larr" Subtract"`
`"Remainder" ->" " 0+color(white)(.)x-5`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So `(x^2-4x+4)/(x^2-5x+9)" "=" "color(magenta)( 1) +(x-5)/(x^2-5x+9)`