Multiply the numerator and denominator by the conjugate of the denominator:

$\displaystyle\frac{{{x}}}{{{\left({x}+\sqrt{{{3}}}\right)}}}\cdot\frac{{{\left({x}-\sqrt{{{3}}}\right)}}}{{{\left({x}-\sqrt{{{3}}}\right)}}}=\frac{{{{x}}^{{2}}-{x}\sqrt{{{3}}}}}{{{{x}}^{{2}}-\sqrt{{{{3}}^{{2}}}}}}=\frac{{{{x}}^{{2}}-{x}\sqrt{{{3}}}}}{{{{x}}^{{2}}-{3}}}\usepackage{cmbright}\Huge\$