lean_workbook_plus_42537

Proved

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

Note that $\frac{1}{1-x_j}-x_j=1+\frac{{x_j}^2}{1-x_j}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_42537  (x j : ℝ)
  (h₀ : x ≠ 1)
  (h₁ : j ≠ 0) :
  1 / (1 - x) - x = 1 + x^2 / (1 - x)   :=  by sorry

Source