Answer
$ \frac{1-3x^2}{2\sqrt x(1+x^2)^2}$
Work Step by Step
$\frac{\frac{1+x^2}{2\sqrt x}-2x\sqrt x}{(1+x^2)^2}=\frac{1+x^2-4x^2}{2\sqrt x(1+x^2)^2}=\frac{1-3x^2}{2\sqrt x(1+x^2)^2}$
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