If $\frac{1}{x+\frac{1}{5}}=\frac{5}{3}$, then $x$ equals
(A) $\frac{2}{5}$
(B) $\frac{4}{5}$
(C) $\frac{1}{5}$
(D) $-\frac{2}{5}$
(E) $-\frac{22}{5}$
Solution 1

Taking the reciprocal of both sides and then solving,

$$
\begin{array}{r}
\frac{1}{x+\frac{1}{5}}=\frac{5}{3} \\
x+\frac{1}{5}=\frac{3}{5} \\
x=\frac{2}{5}
\end{array}
$$

## Solution 2

Cross-multiplying,

$$
\begin{aligned}
\frac{1}{x+\frac{1}{5}} & =\frac{5}{3} \\
5\left(x+\frac{1}{5}\right) & =3 \\
5 x+1 & =3 \\
x & =\frac{2}{5}
\end{aligned}
$$

ANSWER: (A)