How do you combine #x/(x^2+4x-12)+6/(x^2+4x-12)#?

1 Answer
Mar 28, 2018

#(x+6)/(x^2 + 4x -12) = 1/(x-2)#

Explanation:

Given: #x/(x^2 + 4x -12) + 6/(x^2 + 4x -12)#

To combine both terms must have a common denominator. Since both terms have #x^2 + 4x -12# as their denominator, this is the common denominator.

To combine:
#x/(x^2 + 4x -12) + 6/(x^2 + 4x -12) = (x+6)/(x^2 + 4x -12)#

If you need to simplify this expression, realize that the denominator can be factored:

#x^2 + 4x -12 = (x+6)(x-2)#

#(x+6)/(x^2 + 4x -12) = cancel((x+6))/(cancel(x+6)(x-2)) = 1/(x-2)#