Simplify. x-2 / (x^2+4x-12)

Simplifying the above expression we shall proceed as follows:

x-2 / (x^2+4x-12)

factoring out the denominator we get:

x^2+4x-12

=x^2-2x+6x-12

=x (x-2) + 6 (x-2)

= (x+6) (x-2)

thus our expression will be:

(x-2) / [ (x+6) (x-2) ]

simplifying the above we get:

1 / (x+6)

Answer: 1 / (x+6)