Question 11
For any positive real numbers $a$, $b$, $c$, $d$, prove that
$$
\frac{(a+b)^2 + (c+d)^2}{(a^2+c^2)(b+d) + (a+c)(b^2+d^2)} \le \frac{1}{a+c} + \frac{1}{b+d}.
$$
$$
\frac{(a+b)^2 + (c+d)^2}{(a^2+c^2)(b+d) + (a+c)(b^2+d^2)} \le \frac{1}{a+c} + \frac{1}{b+d}.
$$