We can make the fraction $\frac{2 + \frac{3}{n}}{3 + \frac{2}{n}}$ much easier to work with by finding an EQUIVALENT fraction.

Take: $\frac{2 + \frac{3}{n}}{3 + \frac{2}{n}}$

Multiply top and bottom by n to get: $\frac{2n+3}{3n+2}$

So, the original equation becomes: $\frac{2n+3}{3n+2}=\frac{5}{4}$

Cross multiply to get: $4(2n+3)=5(3n+2)$

Expand to get: $8n+12=15n+10$

Subtract 8n from both sides to get: $12=7n+10$

Subtract 10 from both sides to get: $2=7n$

Divide both sides by 7 to get: $\frac{2}{7}=n$

Answer: $\frac{2}{7}$

Cheers,
Brent