To solve the equation, we need to isolate the variable x.

First, let's simplify the left side of the equation by multiplying both the numerator and denominator of the fraction by (x+2):

(x-1)/(x+2) * (x+2)/(x+2) = (x+2)

This simplifies to:

(x-1) = (x+2)(x+2)

Expanding the right side:

(x-1) = (x^2 + 4x + 4)

Now, let's move all terms to one side of the equation:

x - 1 - x^2 - 4x - 4 = 0

Combining like terms:

-x^2 - 3x - 5 = 0

Now, we have a quadratic equation. To solve it, we can either factor it or use the quadratic formula. In this case, the quadratic equation does not factor easily, so we will use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = -1, b = -3, and c = -5. Plugging these values into the quadratic formula:

x = (-(-3) ± √((-3)^2 - 4(-1)(-5))) / (2(-1))

Simplifying:

x = (3 ± √(9 - 20)) / (-2)

x = (3 ± √(-11)) / (-2)

Since we have a negative value under the square root, the equation has no real solutions.