Answer
To do the proof, we simplify the expression:
$\frac{a}{b} = \frac{c}{d} $
We add b/b to one side and d/d to the other, for both of these equal one:
$\frac{a}{b} + \frac{b}{b} = \frac{c}{d} + \frac{d}{d} \\ \frac{a+b}{b} = \frac{c+d}{d} $