show that if $\frac{a}{b} = \frac{c}{d}$ then $\frac{a}{b}=\frac{c}{d} = \frac{a-c}{b-d}$ $\frac{a}{b}=\frac{c}{d} = \frac{a-c}{b-d}$
Precalculus Mathematics in a nutshell says it's easy to verify by cross-multiplication but I'm having difficulty doing so. 
(not a homework problem, any help would be appreciated) 

Substituting $$a=bt,c=dt$$ then $$\frac{a-c}{b-d}=\frac{bt-dt}{b-d}=t$$
