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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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    $\begingroup$ If you evaluate 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 $c$. $\endgroup$
    – MarcoB
    Sep 9, 2020 at 4:30

1 Answer 1

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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]
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