lean_workbook_plus_22402

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

$\frac{x^4+1}{x^6+1}=\frac{1}{3}\frac{x^2+1}{x^4-x^2+1}+\frac{2}{3(x^2+1)}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_22402  (x : ℝ) :
  (x^4 + 1) / (x^6 + 1) = 1 / 3 * (x^2 + 1) / (x^4 - x^2 + 1) + 2 / (3 * (x^2 + 1))   :=  by sorry

Source