[tex]\displaystyle\bf\\\frac{4}{\sqrt{17} -3} =\frac{4\cdot(\sqrt{17} +3)}{(\sqrt{17} -3)\cdot(\sqrt{17} +3)} =\frac{4\cdot(\sqrt{17} +3)}{(\sqrt{17})^{2} -3^{2} } =\\\\\\=\frac{4\cdot(\sqrt{17} +3)}{17-9} =\frac{4\cdot(\sqrt{17} +3)}{8} =\frac{\sqrt{17} +3}{2}[/tex]