$2 \cdot 125$ three machines $P, Q, R$ complete a certain task together in $x$ hours, when $P$ completes this task alone it takes an additional 6 hours, $Q$ takes an additional 1 hour, $R$ takes an additional $x$ hours, then the value of $x$ is
(A) $\frac{2}{3}$.
(B) $\frac{11}{12}$.
(C) $\frac{3}{2}$.
(D) 2 .
(E) 3 .
(13th American High School Mathematics Examination, 1962)
[Solution] From the given, $\frac{1}{x+6}+\frac{1}{x+1}+\frac{1}{x+x}=\frac{1}{x}$, simplifying it yields $3 x^{2}+7 x-6=0$, solving which gives $x=\frac{2}{3}$ or -3 (discard). Therefore, the answer is $(A)$.