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Question Number 140997 by loveineq last updated on 14/May/21

Let a, b, c ⩾ 0 . Prove that

\frac{1}{8} \cdot \frac{(2 + a) (2 + b) (2 + c)}{(1 + a) (1 + b) (1 + c)} ⩾ \frac{4 - a - b - c}{4 + a + b + c}

Commented by MJS_new last updated on 15/May/21

as easy as the last one

all denominators are > 0 \Rightarrow just multiplicate

and subtract rhs from both sides \Rightarrow only

positive terms on lhs

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