[tex]\displaystyle \\
x= \frac{1}{ \sqrt{3}-1 }- \frac{1}{ \sqrt{3}+1 } \\ \\
\texttt{Aducem la acelasi numitor. } \\
\texttt{Numitorul comun este: }~( \sqrt{3}-1 )( \sqrt{3}+1 ) \\ \\
x= \frac{\sqrt{3}+1}{ (\sqrt{3}-1)(\sqrt{3}+1) }- \frac{\sqrt{3}-1}{ (\sqrt{3}+1)(\sqrt{3}-1)} \\ \\
x= \frac{\sqrt{3}+1}{ (\sqrt{3})^2-1^2 }- \frac{\sqrt{3}-1}{ (\sqrt{3})^2-1^2 } [/tex]
[tex]\displaystyle
x= \frac{\sqrt{3}+1 - (\sqrt{3}-1) }{ (\sqrt{3})^2-1^2 }= \frac{\underline{\sqrt{3}}+1 - \underline{\sqrt{3}}+1) }{ 3-1 }= \frac{1+1}{3-1}=\frac{2}{2}=\boxed{1} [/tex]
