An algebra problem by Aman Dubey

Algebra Level 2

Simplify the expression: \( \dfrac{ (a-b)^3 +(b-c)^3 + (c-a)^3}{(a-b)(b-c)(c-a)} \).

Details And Assumptions :

  • \(a\neq b\neq c\)
  • Use :- \( x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy -yz - xz)\)
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