parmenides51 wrote: Prove that if $a,b,c, d \in [1,2]$, then $$\frac{a + b}{b + c}+\frac{c + d}{d + a}\le 4 \frac{a + c}{b + d}$$When does the equality hold? https://artofproblemsolving.com/community/c6h1975066p13703005 Let $a,b,c,d\in[1,3].$ Prove that$$\frac{a+b}{c+d}\left(\frac{a+c}{a+d}+\frac{b+c}{b+d}\right)\leq 6.$$

VERY GOOD QUESTIONS BY SQING