X/x+2 + 6/x-2 = 2x+12/x-4

To solve the equation, we need to find a common denominator for all the fractions. In this case, the common denominator is (x+2)(x-2)(x-4).

Multiplying both sides of the equation by the common denominator, we get:

(x+2)(x-2)(x-4)(X/x+2) + (x+2)(x-2)(x-4)(6/x-2) = (x+2)(x-2)(x-4)(2x+12/x-4)

Simplifying, we have:

X(x-2)(x-4) + 6(x+2)(x-4) = 2x(x+2)(x-2) + 12(x+2)(x-2)

Expanding and combining like terms, we get:

X(x^2 - 6x + 8) + 6(x^2 - 2x - 8) = 2x(x^2 - 4) + 12(x^2 - 4)

Simplifying further, we have:

X(x^2 - 6x + 8) + 6(x^2 - 2x - 8) = 2x^3 - 8x + 12x^2 - 48

Expanding and combining like terms, we get:

X^3 - 6X^2 + 8X + 6X^2 - 12X - 48 = 2X^3 - 8X + 12X^2 - 48

Simplifying, we have:

X^3 - 48 = 2X^3 - 48

Subtracting 2X^3 from both sides, we get:

-X^3 = 0

Dividing both sides by -1, we have:

X^3 = 0

Taking the cube root of both sides, we get:

X = 0

Therefore, the solution to the equation is X = 0.