<s>[INST] How to proof the reason? I have this statement:

If $\frac{a}{b} = \frac{c}{d},$ prove that
  $\frac{a+b}{a-b}=\frac{c+d}{c-d}$

I tried to add 1, multiply 1 and nothing.
My development was:
$\frac{a}{b} - \frac{b}{b} = \frac{c}{d} - \frac{d}{d}$
$\frac{a-b}{b} = \frac{c-d}{d}$
$\frac{b}{a-b} = \frac{d}{c-d}$ (I raised to $^{-1}$)
So far I have arrived, without much success.
How can I prove it? Thanks in advance.
 [/INST] Let, $\frac{a}{b}=\frac{c}{d}=k$ or, $a=bk,c=dk$. Now consider the LHS:$$\frac{a+b}{a-b}=\frac{bk+b}{bk-b}=\frac{k+1}{k-1}$$
Also, $$\frac{c+d}{c-d}=\frac{dk+d}{dk-d}=\frac{k+1}{k-1}~~~~~~~~~\boxed{}$$
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