Chapter 6.4, Problem 3MC

Prove that if $\frac{a}{b}=\frac{c}{d}$ and $a\ne b$, then the following are true.

a. $\frac{a+b}{b}=\frac{c+d}{b}\left(Hint:\frac{a}{b}+1=\frac{c}{d}+1\right)$

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

c. $\frac{a-b}{a+b}=\frac{c-d}{c+d}$

d. $\frac{d}{c-d}=\frac{b}{a-b}$