To solve the equation, we need to simplify both sides and then solve for x.

Starting with the left side of the equation:
x + 2/x - 2 - 1/x

To combine the fractions, we need a common denominator. The common denominator is x(x-2), so we multiply the first fraction by (x-2)/(x-2) and the second fraction by x/(x).

(x(x-2) + 2(x-2) - (x-2))/x(x-2)

Expanding and combining like terms:
(x^2 - 2x + 2x - 4 - x + 2)/x(x-2)
(x^2 - 3x - 2)/x(x-2)

Now, let's simplify the right side of the equation:
2/x(x-2)

To combine the fractions, we need a common denominator. The common denominator is x(x-2), so we multiply the numerator by x(x-2)/x(x-2):

2(x(x-2))/x(x-2)
(2x^2 - 4x)/x(x-2)

Now, our equation becomes:
(x^2 - 3x - 2)/x(x-2) = (2x^2 - 4x)/x(x-2)

To solve for x, we can cross-multiply:
(x^2 - 3x - 2)(x(x-2)) = (2x^2 - 4x)(x(x-2))

Expanding both sides:
x^3 - 2x^2 - 3x^2 + 6x - 2x(x-2) + 4(x-2) = 2x^3 - 4x^2 + 2x^2 - 4x

Simplifying:
x^3 - 2x^2 - 3x^2 + 6x - 2x^2 + 4x - 4x + 8 = 2x^3 - 4x^2 + 2x^2 - 4x

Combining like terms:
x^3 - 7x^2 + 6x + 8 = 2x^3 - 2x^2 - 4x

Moving all terms to one side:
0 = 2x^3 - 2x^2 - 4x - x^3 + 7x^2 - 6x - 8

Combining like terms:
0 = x^3 - 5x^2 - 10x - 8

Now, we have a cubic equation. To solve for x, we can use numerical methods or factoring techniques.