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) $\frac{6 x-1}{3-x}$

Answer

Expert–verified

Hide Steps

Answer

$\boxed{\frac{6x + 11}{3 - x}}$ is the final answer

Steps

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