Answer
$x=\frac{1\pm \sqrt 5}{2}$
Work Step by Step
$\frac{1}{x^{2}}-\frac{1}{x+1}=0$
$\frac{x+1-x^{2}}{x^{2}(x+1)}=0$
$x=\frac{1\pm \sqrt 5}{2}$
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