[Number Theory]
Problem: For positive integers $a$ and $b$, define $f(a, b)=\frac{a}{b}+\frac{b}{a}+\frac{1}{a b}$.

For example, the value of $f(1,2)$ is 3 .
Determine the value of $f(2,5)$.

Solution: By definition, $f(2,5)=\frac{2}{5}+\frac{5}{2}+\frac{1}{2 \cdot 5}=\frac{2 \cdot 2+5 \cdot 5+1}{2 \cdot 5}=\frac{4+25+1}{10}=\frac{30}{10}=3$.

Final answer: 3