Question 23
Prove that, if $x, y \gt 0$, then
$$
0 \lt \frac{x}{x+y^4} + \frac{y}{y+x^4} - \frac{1}{x^2y^2+1} \lt 1.
$$
$$
0 \lt \frac{x}{x+y^4} + \frac{y}{y+x^4} - \frac{1}{x^2y^2+1} \lt 1.
$$
MathNet 2011 Question 23
Math Olympiad Vault · MathNet 2011