X²-6 / x-3 = x/x-3

To solve the equation \[ \frac{x^2 - 6}{x - 3} = \frac{x}{x - 3}, \] we can start by eliminating the denominator on both sides, assuming \(x - 3 \neq 0\): \[ x^2 - 6 = x. \] Next, rearranging the equation gives us: \[ x^2 - x - 6 = 0. \] Now, we can factor the quadratic equation: \[ (x - 3)(x + 2) = 0. \] Setting each factor equal to zero gives us the solutions: \[ x - 3 = 0 \quad \Rightarrow \quad x = 3, \] \[ x + 2 = 0 \quad \Rightarrow \quad x = -2. \] However, we need to consider the restrictions from the original equation. Since we divided by \(x - 3\), we have the restriction that \(x \neq 3\). Therefore, the only valid solution is: \[ \boxed{-2}. \]