Question

How do you simplify `(4x-9)/(2x-3)`?

Answer 1

`(4x-9)/(2x-3)=color(blue)(2-3/(2x-3))color(white)"xxxxx"`...but it is not clear that this is a "simplification"

Explanation:

Since this was asked under "Excluded Values for Rational Expression" perhaps it should be noted that
`color(white)("XXX")(4x-9)/(2x-3)` is not defined if `(2x-3)=0 rarr x=3/2`

Answer 2

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

Explanation:

Given: `(4x-9)/(2x-3)`

Starting the same process as long division (this one is short)

`color(white)("ddddd.ddddd")4x-9`
`color(magenta)(2)(2x-3)-> ul(4x-6larr" Subtract")`
`color(white)("dddddddddddd")0color(magenta)(-3 larr" Remainder")`

`(4x-9)-:(2x-3) = color(magenta)(2-3/(2x-3))`