$\frac{1 + x^{2}}{(1 + x)^{2}} = \frac{1}{2}$

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Solution

$\frac{1 + x^{2}}{(1 + x)^{2}} = \frac{1}{2}$
$2 + 2 x^{2} = 1 + 2 x + x^{2}$
$1 - 2 x + x^{2} = 0$
$(1 - x)^{2} = 0$
$x = 1$

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