Subtract $\frac{6 x-5}{3-x}$ from $\frac{12 x+6}{3-x}$ (A) $\frac{6 x+1}{3-x}$ (B) $\frac{11-6 x}{3-x}$ (C) $\frac{6 x+11}{3-x}$ (D) $\frac{6 x-1}{3-x}$

Step 1 ：Subtract \(\frac{6 x-5}{3-x}\) from \(\frac{12 x+6}{3-x}\) to get \(\frac{12 x+6}{3-x} - \frac{6 x-5}{3-x}\)

Step 2 ：Simplify to \(\frac{12x + 6 - (6x - 5)}{3 - x}\)

Step 3 ：Distribute the negative sign in the numerator to get \(\frac{12x + 6 - 6x + 5}{3 - x}\)

Step 4 ：Combine like terms in the numerator to get \(\frac{6x + 11}{3 - x}\)

Step 5 ：Check the answer by substituting x = 1 into the original expression and the answer, both should yield \(\frac{17}{2}\)

Step 6 ：\(\boxed{\frac{6x + 11}{3 - x}}\) is the final answer