Question

Cum se rezolva asta? $x= \frac{1}{ \sqrt{3}-1 }- \frac{1}{ \sqrt{3}+1 }$ (rezulttaul trebuie sa fie 1, dar mie nu-mi iese.

Answer 1

  
[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]