X2 ——— = 3x ——— 2-x 2-x

To solve the equation \[ \frac{x^2}{3x} = \frac{2-x}{2-x} \] we first simplify each side. 1. The right side simplifies to 1, as long as \(2 - x \neq 0\) (i.e., \(x \neq 2\)). 2. The left side simplifies as follows: \[ \frac{x^2}{3x} = \frac{x}{3} \quad \text{(assuming \(x \neq 0\))} \] So we rewrite the equation as: \[ \frac{x}{3} = 1 \] Next, multiply both sides by 3: \[ x = 3 \] Now we check the conditions we assumed earlier: - \(x \neq 0\) \(\Rightarrow\) \(x = 3\) satisfies this. - \(x \neq 2\) \(\Rightarrow\) \(x = 3\) satisfies this as well. Thus, the solution to the equation is: \[ \boxed{3} \]