lean_workbook_plus_3152

Proved

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

Let $x, y$ be positive real numbers satisfying $x+y=1.$ Prove that $\frac{x}{2x+y}+\frac{y}{x+3y} \leq \frac{3}{5}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_3152 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) (hxy : x + y = 1) : x / (2 * x + y) + y / (x + 3 * y) ≤ 3 / 5   :=  by sorry

Source