It looks like you have an expression involving a ratio or division of two algebraic expressions. The expression \((3x + 2) \div (x - 3)\) can be interpreted as:

\[ \frac{3x + 2}{x - 3} \]

This is a rational function. To simplify or analyze this expression, you might consider the following steps:

1. **Domain**: Determine the values of \(x\) for which the expression is defined. The denominator \(x - 3\) cannot be zero, so \(x \neq 3\).

2. **Simplification**: Check if the numerator and the denominator have any common factors that can be canceled out. In this case, \(3x + 2\) and \(x - 3\) do not have common factors, so the expression is already in its simplest form.

3. **Graphing**: If you want to graph the function \(y = \frac{3x + 2}{x - 3}\), you would note that there is a vertical asymptote at \(x = 3\) and a horizontal asymptote as \(x\) approaches infinity. The horizontal asymptote can be found by considering the degrees of the polynomials in the numerator and the denominator. Since both are linear (degree 1), the horizontal asymptote is the ratio of the leading coefficients, which is \(y = 3\).

4. **Behavior Near Asymptotes**: As \(x\) approaches 3 from the left, the function \(y = \frac{3x + 2}{x - 3}\) will tend to \(-\infty\). As \(x\) approaches 3 from the right, the function will tend to \(+\infty\).

5. **Intercepts**:
- **Y-intercept**: Set \(x = 0\) to find the y-intercept. \(y = \frac{3(0) + 2}{0 - 3} = \frac{2}{-3} = -\frac{2}{3}\).
- **X-intercept**: Set the numerator equal to zero and solve for \(x\). \(3x + 2 = 0 \Rightarrow x = -\frac{2}{3}\).

So, the expression \(\frac{3x + 2}{x - 3}\) is a rational function with a vertical asymptote at \(x = 3\), a horizontal asymptote at \(y = 3\), a y-intercept at \(-\frac{2}{3}\), and an x-intercept at \(-\frac{2}{3}\).