The following equation is being multiplied by the LCD: Complete the multiplication to eliminate the denominators. \( \frac{x+2}{3 x}-\frac{1}{x-2}=\frac{x-3}{3 x} \) \( (3 x)(x-2)\left[\frac{x+2}{3 x}-\frac{1}{x-2}\right]=(3 x)(x-2)\left[\frac{x-3}{3 x}\right] \) The resulting equation is

When you multiply both sides of the equation by the least common denominator (LCD), which is \(3x(x-2)\), you eliminate the denominators. This would look like: \[ (3x)(x-2) \left[\frac{x+2}{3x} - \frac{1}{x-2}\right] = (3x)(x-2)\left[\frac{x-3}{3x}\right] \] Distributing on the left side gives you: \[ (x - 2)(x + 2) - 3x = (x - 3)(x-2) \] This simplifies further to: \[ x^2 - 4 - 3x = x^2 - 5x + 6 \] Removing \(x^2\) from both sides results in: \[ -4 - 3x = -5x + 6 \] Ultimately, rearranging gives you: \[ 2x - 10 = 0 \quad \text{or} \quad x = 5 \] And there you have your resulting equation!