1/x - 1/y = 1/(xy) and xy != 0. Quantity A: x, Quantity B: y

Rationale

Quantity A and Quantity B are equal.

The equation \( \frac{1}{x} - \frac{1}{y} = \frac{1}{xy} \) can be manipulated to show that \( x \) and \( y \) must be equal if \( xy \neq 0 \). This indicates that both quantities are indeed the same under the given conditions.

A (Quantity A is greater.) YOUR ANSWER

This choice suggests that \( x > y \). However, from the derived equation, we find that \( x \) must equal \( y \) to satisfy the equation, making this option incorrect.

B (Quantity B is greater.) YOUR ANSWER

This option implies that \( y > x \). Similar to the previous choice, the equation shows that \( x \) and \( y \) must be equal, which contradicts this assertion.

C (The two quantities are equal.) CORRECT

This choice correctly reflects the conclusion drawn from the equation. By rearranging \( \frac{1}{x} - \frac{1}{y} = \frac{1}{xy} \), we can conclude that \( x = y \), confirming that both quantities are equal.

D (The relationship cannot be determined from the information given.) YOUR ANSWER

This choice suggests that we cannot ascertain the relationship between \( x \) and \( y \). However, the equation allows us to directly derive that \( x \) equals \( y \), making this option incorrect.

Conclusion

The equation \( \frac{1}{x} - \frac{1}{y} = \frac{1}{xy} \) leads us to the conclusion that \( x \) and \( y \) are equal when \( xy \neq 0 \). Therefore, Quantity A and Quantity B are indeed equal, making option C the correct choice. Understanding the relationships defined in algebraic equations is crucial for accurately determining quantity comparisons.

1/x - 1/y = 1/(xy) and xy != 0. Quantity A: x, Quantity B: y

Quantity A and Quantity B are equal.

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