They are asking us to add the three fractions $\dfrac{1}{a}$, $\dfrac{1}{b}$, and $\dfrac{1}{c}$ using a common denominator of $abc$. This means the equivalent fractions will be $\dfrac{bc}{abc}$, $\dfrac{ac}{abc}$, and $\dfrac{ab}{abc}$, and their sum would be equivalent to $\dfrac{bc+ac+ab}{abc}$, which is what leads to the numerator of $bc+ac+ab$.

kevinying says

hhhh

Quinn Novick says

For number 57, why is the numerator bc+ac+bc? Thank you.

Dabral says

They are asking us to add the three fractions $\dfrac{1}{a}$, $\dfrac{1}{b}$, and $\dfrac{1}{c}$ using a common denominator of $abc$. This means the equivalent fractions will be $\dfrac{bc}{abc}$, $\dfrac{ac}{abc}$, and $\dfrac{ab}{abc}$, and their sum would be equivalent to $\dfrac{bc+ac+ab}{abc}$, which is what leads to the numerator of $bc+ac+ab$.