lean_workbook_plus_81216

Proved

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

给出分式 $\frac{x^2-2}{(x-1)^3}$ 的分解结果： $- \left( x-1 \right) ^{-3}+2\, \left( x-1 \right) ^{-2}+ \left( x-1 \right) ^{-1}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_81216 (x : ℝ) (hx : x ≠ 1) : (x^2 - 2) / (x - 1)^3 = -1 / (x - 1)^3 + 2 / (x - 1)^2 + 1 / (x - 1)   :=  by sorry

Source