Answer
$\color{blue}{\dfrac{\sqrt{15}-3}{2}}$
Work Step by Step
Rationalize the denominator by multiplying the conjugate of the denominator, which is $\sqrt5-\sqrt3$, to both the numerator and the denominator to obtain:
$=\dfrac{\sqrt3(\sqrt5-\sqrt3)}{(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)}$
Distribute $\sqrt3$ in the numerator and use the formula $(a+b)(a-b)=a^2-b^2$ to simplify the denominator to obtain:
$=\dfrac{\sqrt{15}-\sqrt{9}}{(\sqrt5)^2-(\sqrt3)^2}
\\=\dfrac{\sqrt{15}-3}{5-3}
\\=\color{blue}{\dfrac{\sqrt{15}-3}{2}}$
