lean_workbook_plus_9700

Proved

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

Let $a,b$ be positive real numbers , prove that $\frac{1}{a}+\frac{2}{a+b}\le \frac{9}{8}(\frac{1}{a}+\frac{1}{b})$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_9700 : ∀ a b : ℝ, a > 0 ∧ b > 0 → (1 / a + 2 / (a + b) : ℝ) ≤ 9 / 8 * (1 / a + 1 / b)   :=  by sorry

Source