If $\frac{x}{y} = \frac{3}{4}$, then find the value of $\frac{2x + 3y}{2x - y}$.

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**Solution:**

1. Given: $\frac{x}{y} = \frac{3}{4}$.

2. Express $x$ in terms of $y$:
   $$x = \frac{3}{4} y$$

3. Substitute $x = \frac{3}{4} y$ into the expression:
   $$\frac{2x + 3y}{2x - y} = \frac{2 	imes \frac{3}{4} y + 3y}{2 	imes \frac{3}{4} y - y}$$

4. Simplify numerator:
   $$2 	imes \frac{3}{4} y = \frac{6}{4} y = \frac{3}{2} y$$
   So numerator = $\frac{3}{2} y + 3y = \frac{3}{2} y + \frac{6}{2} y = \frac{9}{2} y$

5. Simplify denominator:
   $$2 	imes \frac{3}{4} y = \frac{6}{4} y = \frac{3}{2} y$$
   So denominator = $\frac{3}{2} y - y = \frac{3}{2} y - \frac{2}{2} y = \frac{1}{2} y$

6. Therefore,
   $$\frac{2x + 3y}{2x - y} = \frac{\frac{9}{2} y}{\frac{1}{2} y} = \frac{9}{2} 	imes \frac{2}{1} = 9$$

**Answer:** $9$

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