If $\frac{1}{x+3}=2$, then the value of $\frac{1}{x+5}$ is
(A) $\frac{1}{2}$
(B) $\frac{2}{3}$
(C) $\frac{2}{5}$
(D) $\frac{1}{4}$
(E) 4
Since $\frac{1}{x+3}=2$, then, taking reciprocals of both sides, $x+3=\frac{1}{2}$.

Since $x+3=\frac{1}{2}$, then $x+5=\frac{1}{2}+2=\frac{5}{2}$.

Since $x+5=\frac{5}{2}$, then $\frac{1}{x+5}=\frac{2}{5}$.

(Notice that we did not need to actually find the value of $x$.)

ANSWER: (C)