lean_workbook_plus_21470

import Mathlib.Analysis.Complex.Basic

theorem lean_workbook_plus_21470 (a b : ℝ) (f : ℝ → ℝ) (h1 : ∀ x, f x ≠ 0) (h2 : ∀ x, x ≠ 0) : (∀ ε > 0, ∃ N : ℕ, ∀ x > N, |f x - (a * x + b)| < ε) → ∀ ε > 0, ∃ N : ℕ, ∀ x > N, |f x / x - a| < ε   :=  by sorry