Elementary Geometry for College Students (6th Edition)

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: $\frac{a}{b} + \frac{b}{b} = \frac{c}{d} + \frac{d}{d} \\ \frac{a+b}{b} = \frac{c+d}{d}$