If `a/b=c/d` then

Options

A. `(a+b)/(a-b)=(c+d)/(c-d)`
B. `(a+b)/(a^(2))=(c+d)/(d^(2))`
C. `(a+b)/(a^(2))=(c+d)/(c^(2))`
D. `ac=bd`

Answer

To solve the problem, we start with the given proportion:

**Given:**
\[ \frac{a}{b} = \frac{c}{d} \]

### Step 1: Apply the Compando and Divendo Rule
We will apply the compando and divendo rule to the given proportion. This rule states that if two ratios are equal, we can add or subtract the numerators and denominators to form new ratios.

**Applying the rule:**
From the given proportion, we can write:
\[ \frac{a + b}{a - b} = \frac{c + d}{c - d} \]

### Step 2: Identify the Correct Option
Now, we compare this result with the options provided in the question.

**Options:**
1. \(\frac{A + B}{A - B} = \frac{C + D}{C - D}\)
2. \(\frac{A + B}{A^2} = \frac{C + D}{D^2}\)
3. \(\frac{A + B}{A^2} = \frac{C + D}{C^2}\)
4. \(AC = BD\)

From our derived equation, we see that it matches with **Option 1**.

### Conclusion
Thus, the correct answer is:
\[ \text{Option 1: } \frac{A + B}{A - B} = \frac{C + D}{C - D} \]

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