Question

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

Answer 1

`(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)`