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