Given real-valued terms $a,b,c \in {R}$ with the following conditions on them: $ 0 \leq a \leq 1 $, $|b|<1$, and $|c|< 1$. And given the terms $ X= \frac{1}{1-( (1-a)b + ac )}$ and $ Y =\frac{1}{1-b}$, are these two terms related via some inequality like $X\leq Y$? Does this inequality hold true all the time or does it need conditions to be true? I am trying to prove an interesting relation here, so was wondering if someone here could give me some tips or suggestions? (This is not homework).
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1$\begingroup$ If $c > b$, then $X>Y$. If $c < b$, then $X<Y$. If $c=b$, then $X=Y$. $\endgroup$– amsmathApr 17, 2019 at 13:23
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It's wrong. Try $a=b=\frac{1}{2}$ and $c=1$.
answered Apr 17, 2019 at 14:04