Explanation

As printed in the official paper, the left side is (3x−6)/[(x−6)(x+k)] (this file's question text has it inverted — a data error). Combining the right side over (x−6)(x+k) gives [2(x+k) + (x−6)]/[(x−6)(x+k)] = (3x+2k−6)/[(x−6)(x+k)]. Equating numerators: 3x − 6 = 3x + 2k − 6, so k = 0. Hence option A.