# Algebraic manipulation and inequality

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).

• If $c > b$, then $X>Y$. If $c < b$, then $X<Y$. If $c=b$, then $X=Y$. – amsmath Apr 17 '19 at 13:23

It's wrong. Try $$a=b=\frac{1}{2}$$ and $$c=1$$.