B: \( \frac{x+6}{2 x-6} \div \frac{5 x+30}{6 x-18} \)

To simplify the expression, start by rewriting the division as multiplication by the reciprocal: \[ B: \frac{x+6}{2x-6} \cdot \frac{6x-18}{5x+30} \] Now, factor each part: 1. \( 2x - 6 = 2(x - 3) \) 2. \( 6x - 18 = 6(x - 3) \) 3. \( 5x + 30 = 5(x + 6) \) Substituting the factors back into the expression gives: \[ = \frac{x + 6}{2(x - 3)} \cdot \frac{6(x - 3)}{5(x + 6)} \] Next, you can cancel the common factors \(x + 6\) and \(x - 3\): \[ = \frac{6}{2 \cdot 5} = \frac{6}{10} = \frac{3}{5} \] Thus, the simplified expression is: \[ B = \frac{3}{5} \]