2025 · Q36
What is ((a-b)²)/((b-c)(c-a))+((b-c)²)/((c-a)(a-b))+((c-a)²)/((a-b)(b-c)) - 3 equal to, where ≠?
Elementary MathematicsAlgebra
- A0
- B3
- Ca + b + c
- D3 (a−b) (b−c) (c−a)
Explanation
Putting the three fractions over the common denominator (a−b)(b−c)(c−a), the numerator becomes (a−b)³ + (b−c)³ + (c−a)³. Since (a−b) + (b−c) + (c−a) = 0, the identity u³+v³+w³ = 3uvw applies, giving 3(a−b)(b−c)(c−a). The expression is therefore 3 − 3 = 0, option (a).