Question

If \( pqr = 1 \), the value of the expression \[ \frac{1}{1 + p + q} + \frac{1}{1 + q + r} + \frac{1}{1 + r + p} \] is equal to:

• A. \( p + q + r \)
• B. \( \frac{1}{p + q + r} \)
• C. 1
• D. \( p^{-1} + q^{-1} + r^{-1} \)

Hint:

For problems with products and sums, try simplifying the expressions algebraically.

Answer 1

The Correct Option is C

Given that \( pqr = 1 \), we substitute into the expression: \[ \frac{1}{1 + p + q} + \frac{1}{1 + q + r} + \frac{1}{1 + r + p}. \] The sum of these fractions simplifies to 1. Thus, the Correct Answer is 1.