Explanation

From 1/x=1/p+1/q=(p+q)/pq we get x=pq/(p+q). Substituting, (x+p)/(x−p)=−(p+2q)/p and (x+q)/(x−q)=−(2p+q)/q, so their difference is −2q/p+2p/q=2(p²−q²)/pq. Multiplying by the prefactor pq/(p²−q²) cancels everything to leave 2, option D. The trap is mis-simplifying (x+p)/(x−p) by forgetting the common denominator.