To solve this equation, we need to first find a common denominator for all the fractions.

Given expression: 2x - 2/(x + 3) - 18/(x^2 - 9) = (x - 6)/(x - 3)

Rewrite -18/(x^2 - 9) as -18/(x + 3)(x - 3), since x^2 - 9 = (x + 3)(x - 3)

Now, the equation becomes:

2x - 2/(x + 3) - 18/(x + 3)(x - 3) = (x - 6)/(x - 3)

To find a common denominator, we need to multiply the first term by (x - 3)/(x - 3) and the second term by 1:

(2x(x - 3) - 2(x - 3))/(x + 3)(x - 3) - 18/(x + 3)(x - 3) = (x - 6)/(x - 3)

Simplify the expression:

(2x^2 - 6x - 2x + 6 - 18)/(x + 3)(x - 3) = (x - 6)/(x - 3)

Combine like terms:

(2x^2 - 8x - 12)/(x + 3)(x - 3) = (x - 6)/(x - 3)

Now we can simplify the equation further, but we need to first factor the numerator:

(2(x^2 - 4x - 6))/(x^2 - 9) = (x - 6)/(x - 3)

Now the equation becomes:

2(x^2 - 4x - 6)/(x^2 - 9) = (x - 6)/(x - 3)

At this point, we can cross multiply to solve the equation. After solving the equation, we can verify our solution by substituting it back into the original equation.