Dividing a quadratic by a linear expression

Proved

WorkbookSource.problem_54150

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

$(a^2+1)/(a+k)=a-k+(k^2+1)/(a+k)$

Source: InternLM Lean-Workbook, record lean_workbook_54150 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_54150 (a k : ℝ) (h : a ≠ -k) : (a^2 + 1) / (a + k) = a - k + (k^2 + 1) / (a + k)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_54150; Apache-2.0

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