To solve this equation, we first need to find a common denominator on the left side of the equation:

(x^2 + 2x - 8)/(x^2 - 4) = 7/(x + 2)

We know that x^2 - 4 can be factored as (x + 2)(x - 2), so the equation becomes:

(x^2 + 2x - 8)/((x + 2)(x - 2)) = 7/(x + 2)

Next, we can simplify the left side of the equation by factoring the numerator:

((x + 4)(x - 2))/((x + 2)(x - 2)) = 7/(x + 2)

Now, we can cancel out the common factor of x - 2 from the numerator and denominator on the left side of the equation:

(x + 4)/(x + 2) = 7/(x + 2)

We are left with:

x + 4 = 7

Now, we can solve for x:

x = 7 - 4
x = 3

Therefore, the solution to the equation is x = 3.