Question

What is the denominator that would make this equation true: `\frac { x ^ { 2} - x - 6} { ?} = x - 3`?

Answer 1

`(x+2)`

Explanation:

First factor the numerator (here is one method):

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

So we have `((x+2)(x-3))/?=x-3`

So we want the missing term to divide away with `(x+2)`, which means it must also be `(x+2)`

If it is `(x+2)`,

`((x+2)(x-3))/(x+2)=(x-3)->(cancel((x+2))(x-3))/cancel((x+2))=(x-3)`

`(x-3)/1=(x-3)`