Question

How do you divide `(9-16x^2) / (4x-3)`?

Answer 1

`(9-16x^2)/(4x-3) = -(4x+3)`
`color(white)("XXXX")` `color(white)("XXXX")`(assuming `4x-3 != 0`)

Explanation:

`9-16x` is the difference of squares and therefore can be factored as:
`color(white)("XXXX")` `9-16x^2 = (3-4x)(3+4x)`
`color(white)("XXXX")`or
`color(white)("XXXX")`9-16x^2 = (-1)(4x-3)(4x+3)#

So
`color(white)("XXXX")` `(9-16x^2)/(4x-3)`
`color(white)("XXXX")` `color(white)("XXXX")` `= ((-1)cancel((4x-3))(4x+3))/(cancel(4x-3))`

`color(white)("XXXX")` `color(white)("XXXX")` `= -(4x+3)`