[tex]\displaystyle\\
\frac{1}{ \sqrt{8} - \sqrt{x} } + \frac{1}{ \sqrt{8} + \sqrt{x} } =\\\\\\
= \frac{ \sqrt{8} + \sqrt{x} +\sqrt{8} - \sqrt{x} }{ (\sqrt{8} - \sqrt{x})(\sqrt{8} -\sqrt{x})}= \\\\\\
= \frac{ \sqrt{8} +\sqrt{8} }{ 8 - x}= \frac{ 2\sqrt{8}}{ 8 - x}=\frac{ 4\sqrt{2}}{ 8 - x}\\\\\\
\frac{ 4\sqrt{2}}{ 8 - x}=\frac{ 4\sqrt{2}}{ 3}\\\\\\
\Longrightarrow~~8-x = 3
\Longrightarrow~~x = 8-3 = \boxed{\bf 5}
[/tex]
