(2x - 1)/(x + 3) = (x + 2)/(x - 1) denklemini sağlayan x değerlerinin toplamı kaçtır?

The given equation is:

$$\frac{2x - 1}{x + 3} = \frac{x + 2}{x - 1}$$

Multiply both sides by $(x+3)(x-1)$ to clear the denominators, assuming $x \neq -3$ and $x \neq 1$:

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

Expand the left side:

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

Expand the right side:

$$(x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6$$

Now the equation is:

$$2x^2 - 3x + 1 = x^2 + 5x + 6$$

Move all terms to one side to get a quadratic equation in the form $ax^2 + bx + c = 0$:

$$2x^2 - x^2 - 3x - 5x + 1 - 6 = 0$$ $$x^2 - 8x - 5 = 0$$

For a quadratic equation $ax^2 + bx + c = 0$, the sum of the roots ($x_1 + x_2$) is given by the formula $-\frac{b}{a}$.
In our equation $x^2 - 8x - 5 = 0$, we have $a=1$, $b=-8$, and $c=-5$.
The sum of the roots is:

$$x_1 + x_2 = -\frac{-8}{1} = 8$$

We should also verify that the roots are not $x=-3$ or $x=1$. The discriminant is $\Delta = b^2 - 4ac = (-8)^2 - 4(1)(-5) = 64 + 20 = 84$. Since $\Delta > 0$, there are two distinct real roots. The roots are $x = \frac{8 \pm \sqrt{84}}{2} = 4 \pm \sqrt{21}$. Neither of these values is $-3$ or 1, so both are valid solutions.

The sum of the $x$ values that satisfy the equation is $\boxed{8}$.