Question 103
Let $x, y$ be positive real numbers such that $x + y = 1$. Prove that
$$
\frac{x}{x^2 + y^3} + \frac{y}{x^3 + y^2} \le 2 \left( \frac{x}{x+y^2} + \frac{y}{x^2 + y} \right).
$$
$$
\frac{x}{x^2 + y^3} + \frac{y}{x^3 + y^2} \le 2 \left( \frac{x}{x+y^2} + \frac{y}{x^2 + y} \right).
$$