Question

How do you divide `(x^2-5x-14)/(x-7)div(x+2)/(x^2-9)`?

Answer 1

Dividing is the same as multiplying by the reciprocal.

So
`(x^2-5x-14)/(x-7) div (x+2)/(x^2-9)`
is the same as
`(x^2-5x-14)/(x-7) xx (x^2-9)/(x+2)`

We can simplify this by factoring

`((x-7)(x+2))/(x-7)xx(x^2-9)/(x+2)`

`(cancel(color(red)((x-7)))cancel(color(blue)((x+2))))/cancel(color(red)((x-7)))xx(x^2-9)/cancel(color(blue)((x+2))`

`= x^2-9`