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