let's use A and B (easier to type) you start with $\frac{1}{A} + \frac{1}{B}$ to add the fractions you need a common denominator AB you can multiply the first fraction by B/B and the second by A/A $\frac{1}{A} \cdot \frac{B}{B} + \frac{1}{B} \cdot \frac{A}{A} = \frac{B}{AB}+\frac{A}{AB}= \frac{B+A}{AB}$ another way to do this is to multiply the fractions by AB/AB $\frac{AB}{AB} \left( \frac{1}{A} + \frac{1}{B}\right)$ if we distribute we get $\frac{1}{A} \cdot \frac{AB}{AB}+ \frac{1}{B}\cdot \frac{AB}{AB}$ which gives $\frac{B}{AB}+ \frac{A}{AB}$ The idea of multiplying by AB/AB (clearing the denominator) is just a way to add the fractions