The problem asks us to make $x$ the subject of the formula $x = \frac{3+x}{y}$.

1. Problem Description

The problem asks us to make $x$ the subject of the formula $x = \frac{3+x}{y}$.

2. Solution Steps

We need to isolate $x$ on one side of the equation.

First, multiply both sides of the equation by $y$:

$xy = 3+x$

Next, subtract $x$ from both sides:

$xy - x = 3$

Factor out $x$ from the left side:

$x(y-1) = 3$

Finally, divide both sides by $(y-1)$:

$x = \frac{3}{y-1}$

3. Final Answer

$x = \frac{3}{y-1}$