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What is the proof that $\frac{a+b}{a-b}=\frac{c+d}{c-d}$ given that $\frac{a}{b}=\frac{c}{d}$ Here's what I've got so far:

$$\begin{array}{l} \text{Statements} &&&&&&&&&&&&&&&& \text{Reasons} \\\\ \ \text{1.} \frac{a}{b}=\frac{c}{d} &&&&&&&&&&&&&&&& \text{1. given} \\ \\ \ \text{2.} \frac{a+b}{b} = \frac{c+d}{d} &&&&&&&&&&&&&&&& \text{2. addition transformation}\\ \end{array}$$

After this, I'm not really sure how to get the denominators to a-b and c-d, respectively.

Daniel
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1 Answers1

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Well, for the reason for 2. I'd write 'add one'.

Similarly, we can have 3. $\displaystyle\frac{a-b}b=\frac{c-d}d$. Then divide equation 2. by equation 3.
(You have to separately handle the cases when any denominator would become zero.)

Berci
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