To solve this equation, we first need to get rid of the fractions by multiplying both sides of the equation by the common denominator, which is x + 2.

(x + 2)(x + 2)/-4 = -9(x + 2)/x + 2

Expanding both sides:

(x^2 + 4x + 4)/-4 = -9(x + 2)/x + 2

Simplifying further:

-(x^2 + 4x + 4)/4 = -9(x + 2)/x + 2

Multiplying both sides by -4 to get rid of the negative sign:

x^2 + 4x + 4 = 36(x + 2)/x + 2

Expanding the right side:

x^2 + 4x + 4 = 36x + 72

Rearranging the equation to set it equal to zero:

x^2 + 4x + 4 - 36x - 72 = 0

x^2 - 32x - 68 = 0

Now, we can solve this quadratic equation using the quadratic formula:

x = (-(-32) ± √((-32)^2 - 4(1)(-68))) / 2(1)
x = (32 ± √(1024 + 272)) / 2
x = (32 ± √1296) / 2
x = (32 ± 36) / 2

Therefore, the solutions to the equation are:

x = (32 + 36) / 2 = 68 / 2 = 34
x = (32 - 36) / 2 = -4 / 2 = -2

So, the solutions to the equation are x = 34 and x = -2.