Consider the expression
$\qquad 2(1-2c)/(c-1)^2$
where $c < 0$.
I would like to know if it is bigger than 1 anywhere in its domain.
2(1-2c)/(c-1)^2
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1 Answer
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The function range of your expression (let's say, $y$) is $0 < y < 2$, which can be shown by
FunctionRange[{2 (1 - 2 c) / (c - 1)^2, c < 0}, c, y]
To get the point where $y = 1$,
Solve[2 (1 - 2 c) / (c - 1)^2 == 1 && c < 0, c]
For completeness: as already MarcoB mentioned in his comment, you can get the range where $y > 1$ (or $y < 1$) by Reduce:
Reduce[2 (1 - 2 c) / (c - 1)^2 > 1 && c < 0]
Reduce[2 (1 - 2 c) / (c - 1)^2 < 1 && c < 0]
Reduce[{2 (1 - 2 c) / (c - 1)^2 > 1, c < 0}], you will see that your expression is larger than 1 only in a certain range of negative values of $c$. $\endgroup$