2018 · Q19
What is the value of 1/(1 + x^{b-a} + x^{c-a}) + 1/(1 + x^{a-b} + x^{c-b}) + 1/(1 + x^{a-c} + x^{b-c}), where x ≠ 0?
Elementary MathematicsAlgebra
- A-1
- B0
- C1
- D3
Explanation
Multiply numerator and denominator of the three fractions by xᵃ, xᵇ and xᶜ respectively. The sum becomes (xᵃ + xᵇ + xᶜ)/(xᵃ + xᵇ + xᶜ) = 1, option (C). This is the standard cyclic-exponent identity.