2017 · Q34
What is ((x-y)(y-z)(z-x))/((x-y)³+(y-z)³+(z-x)³) equal to ?
Elementary MathematicsAlgebra
- A-1/3
- B1/3
- C3
- D-3
Explanation
Let A = x−y, B = y−z, C = z−x; then A+B+C = 0. The identity A³+B³+C³ = 3ABC (valid exactly when A+B+C = 0) gives the ratio ABC/(3ABC) = 1/3. Hence option (B) 1/3.