Introduction
In this problem, we are given an equation involving fractions and we are asked to find the values of x that satisfy the equation.

Simplifying the Equation
The first step in solving this problem is to simplify the equation by finding a common denominator for all the fractions. In this case, the common denominator is (x-2)(x+2)(x-3). After we multiply all the fractions by this common denominator, we get:

(x+2)(x-3) - (x-2)^2 = (x-1)(x-2)(x+2) - (x+2)(x-2)(x-3)

Simplifying Further
Next, we can simplify this equation by expanding all the products and combining like terms. After doing this, we get:

x^3 - 6x^2 - 2x + 12 = -x^3 + 3x^2 + 18x - 24

Bringing Like Terms Together
Now, we can bring all the x terms to one side of the equation and all the constant terms to the other side. After doing this, we get:

2x^3 - 9x^2 - 20x + 36 = 0

Factoring
Finally, we can factor this equation and solve for x. After factoring, we get:

(2x-3)(x-4)(x+3) = 0

Therefore, the values of x that satisfy the equation are x = 3/2, x = 4, and x = -3.

Conclusion
In conclusion, we can solve this problem by simplifying the equation, bringing like terms together, factoring, and solving for x. The values of x that satisfy the equation are x = 3/2, x = 4, and x = -3.