a/b + b/a Trick

When adding a fraction and its reciprocal, $\frac{a}{b} + \frac{b}{a}$, you can use the formula:

$\frac{a}{b} + \frac{b}{a} = 2 + \frac{(a-b)^2}{ab}$

For example, $\frac{5}{7} + \frac{7}{5} = 2 + \frac{(7-5)^2}{7 \cdot 5} = 2 + \frac{4}{35} = 2\frac{4}{35}$.

A popular variation involves a slight modification, like $\frac{11}{13} + \frac{2}{11}$. This can be rewritten as $(\frac{11}{13} + \frac{13}{11}) - \frac{11}{11}$, allowing you to use the trick and then adjust the result.