To determine if the equation $ \frac{AB}{CD} = \frac{A \cdot C}{B \cdot D} $ is true, we can simplify both sides and analyze them.

### Break Down the Problem
1. Understand the left side: $ \frac{AB}{CD} $
2. Understand the right side: $ \frac{A \cdot C}{B \cdot D} $

### Relevant Concepts
1. **Rational Expressions**: A rational expression is any expression that can be expressed as a fraction where both the numerator and the denominator are polynomials.
2. **Simplification**: Both sides of the equation can be simplified to see if they are equivalent.

### Analysis and Detail
1. Starting with the left side:
$$
\frac{AB}{CD}
$$

2. The right side:
$$
\frac{A \cdot C}{B \cdot D}
$$

3. Cross-multiplying both sides (to verify if they are equal):
$$
AB \cdot B \cdot D = A \cdot C \cdot CD
$$

4. This can be rearranged:
$$
A B^2 D = A C D
$$
According to this equation, the terms will only be equal if additional constraints hold, specifically if $ B^2 = C $ when both $ A $ and $ D $ are non-zero.

### Verify and Summarize
1. The comparison leads us to understand that unless specific conditions about $ A, B, C, D $ are true, the equality as stated does not hold universally.
2. Hence, we conclude that the statement is false in a general case.

### Final Answer
B. False

Question

To determine if the equation $ \frac{AB}{CD} = \frac{A \cdot C}{B \cdot D} $ is true, we can simplify both sides and analyze them.

### Break Down the Problem
1. Understand the left side: $ \frac{AB}{CD} $
2. Understand the right side: $ \frac{A \cdot C}{B \cdot D} $

### Relevant Concepts
1. **Rational Expressions**: A rational expression is any expression that can be expressed as a fraction where both the numerator and the denominator are polynomials.
2. **Simplification**: Both sides of the equation can be simplified to see if they are equivalent.

### Analysis and Detail
1. Starting with the left side:
   $$
   \frac{AB}{CD}
   $$

2. The right side:
   $$
   \frac{A \cdot C}{B \cdot D}
   $$

3. Cross-multiplying both sides (to verify if they are equal):
   $$
   AB \cdot B \cdot D = A \cdot C \cdot CD
   $$

4. This can be rearranged:
   $$
   A B^2 D = A C D
   $$
   According to this equation, the terms will only be equal if additional constraints hold, specifically if $ B^2 = C $ when both $ A $ and $ D $ are non-zero.

### Verify and Summarize
1. The comparison leads us to understand that unless specific conditions about $ A, B, C, D $ are true, the equality as stated does not hold universally.
2. Hence, we conclude that the statement is false in a general case.

### Final Answer
B. False

Knowee AI · Accepted Answer