Step 1: Determine the common denominator. The denominator is $x(2x + 3)$. Rewrite the expression: \[ \frac{4(2x + 3) - 5x}{x(2x + 3)} = 3. \] Step 2: Simplify the numerator. \[ \frac{8x + 12 - 5x}{x(2x + 3)} = 3 \implies \frac{3x + 12}{x(2x + 3)} = 3. \] Step 3: Perform cross-multiplication. \[ 3x + 12 = 3x(2x + 3) \implies 3x + 12 = 6x^2 + 9x. \] Rearrange the equation: \[ 6x^2 + 6x - 12 = 0. \] Simplify the equation: \[ x^2 + x - 2 = 0. \] Step 4: Solve the quadratic equation by factorization. \[ x^2 + x - 2 = (x + 2)(x - 1) = 0. \] The solutions are $x = -2$ or $x = 1$. Step 5: Verify the solutions. For $x = -2$, the denominator $2x + 3$ becomes $2(-2) + 3 = -4 + 3 = -1$. Therefore, $x = -2$ results in an undefined denominator. The valid solution is $x = 1$. Correct Answer: $x = 1$.