To simplify the expression `(x+6)/(x^2+4x-12)`, first identify that the denominator can be factored based on the coefficients provided. After factoring the denominator, check if any terms in the numerator can cancel out similar terms in the denominator. This process will involve recognizing common factors between the numerator and the denominator, simplifying the expression to its most reduced form.

`1/(x-2)`

Start by factoring both the numerator and the denominator of the expression. Look for factors that are common in both the numerator and the denominator, as these can be cancelled out to simplify the expression

`((x+9)(x+7))/(x(x+7)(x+2)) = (x+9)/(x(x+2))`