Solving a product equation for its second variable

Proved

WorkbookSource.problem_16851

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

lean-workbooksource-checked

Combine all the fractions to get:

$\frac{y+x^{2}+1}{xy}=1$ .

Solving for $y$ gives:

$y=\frac{x^{2}+1}{x-1}$ .

Source: InternLM Lean-Workbook, record lean_workbook_16851 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_16851  (x y : ℝ)
  (h₀ : x ≠ 1)
  (h₁ : x * y ≠ 0)
  (h₂ : (x - 1) * y = x * x + 1) :
  y = (x * x + 1) / (x - 1)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_16851; Apache-2.0

View graph