A weighted reciprocal sum comparison with constant twenty-five twelfths

Proved

WorkbookSource.base_34964

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b$ be positive real numbers , prove that $\frac{2}{a}+\frac{3}{a+b}\le \frac{25}{12}(\frac{1}{a}+\frac{1}{b})$

Source: InternLM Lean-Workbook, record lean_workbook_34964 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_34964 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : (2 / a + 3 / (a + b)) ≤ 25 / 12 * (1 / a + 1 / b)  :=  by sorry

Source