Solve for X in the Equation x/(3+2x) = 1/5: Rational Expression Problem

To solve the equation $\frac{x}{3+2x} = \frac{1}{5}$, we will perform the following steps:

• Step 1: Cross-multiply to eliminate the fractions.
• Step 2: Simplify the resulting equation and solve for $x$.

Now, let's work through these steps:

Step 1: Cross-multiply the equation $\frac{x}{3+2x} = \frac{1}{5}$ to obtain:

$5x = 1(3 + 2x)$

Step 2: Distribute the 1 on the right-hand side:

$5x = 3 + 2x$

Subtract $2x$ from both sides to begin isolating $x$:

$5x - 2x = 3$

$3x = 3$

Divide both sides by 3 to solve for $x$:

$x = \frac{3}{3}$

$x = 1$

Therefore, the solution to the problem is $\boxed{1}$.

The correct answer, matching the given choices, is therefore choice $2$.