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)#