Answer
$\frac{1}{\sqrt{1-x^{2}}}$
Work Step by Step
After squaring, we find a common denominator for the fractions, add them, and simplify:
$\displaystyle \sqrt{1+(\frac{x}{\sqrt{1-x^{2}}})^{2}}=\sqrt{1+\frac{x^{2}}{1-x^{2}}}=\sqrt{\frac{1-x^{2}}{1-x^{2}}+\frac{x^{2}}{1-x^{2}}}=\sqrt{\frac{1}{1-x^{2}}}=\frac{1}{\sqrt{1-x^{2}}}$
