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

1 Answer
Oct 12, 2017

(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)