( [tex] \frac{ \sqrt{3} }{2} [/tex] - [tex] \frac{3 \sqrt{2} + 1}{ \sqrt{3} } [/tex] + [tex] \frac{1}{ \sqrt{2} } [/tex] ) : ( [tex] \frac{1}{ 2\sqrt{3} } [/tex] - [tex] \frac{1}{ \sqrt{2} } [/tex] ) =
[ Amplificam prima fractie cu [tex] \sqrt{6} [/tex] ; a 2-a cu [tex] 2\sqrt{2} [/tex] ; a3-a fractie cu [tex] 2\sqrt{3} [/tex] ; a4-a cu [tex] \sqrt{2} [/tex] ; a 5- a cu [tex] 2\sqrt{3} [/tex] ]
= [tex] \frac{ \sqrt{18} - 6\sqrt{4} - 2\sqrt{2} + 2\sqrt{3} }{ 2\sqrt{6} } : ( \frac{ \sqrt{2} - 2\sqrt{3} }{ 2\sqrt{6} } )[/tex] =
= [tex] \frac{3 \sqrt{2} - 12 - 2\sqrt{2} + 2\sqrt{3} } {2 \sqrt{6} } [/tex] · [tex] \frac{2 \sqrt{6} }{ \sqrt{2} - 2 \sqrt{3} } [/tex] =
[ Aici se simplifica cu [tex] 2\sqrt{6} [/tex] ]
= [tex] \frac{ \sqrt{2}- 12 + 2 \sqrt{3} }{ \sqrt{2} - 2 \sqrt{3} } [/tex] =
[ Rationalizam cu [tex] \sqrt{2} + 2 \sqrt{3} [/tex]]
= [tex] \frac{ (\sqrt{2} + 2 \sqrt{3} - 12)( \sqrt{2} + 2 \sqrt{3} )} { ( \sqrt{2} )^{2} - (2 \sqrt{3} )^{2} } [/tex] =
= [tex] \frac{2 + 2 \sqrt{6} + 2 \sqrt{6} + 12 - 12 \sqrt{2} - 24 \sqrt{3} }{2 - 12} [/tex] =
= [tex] \frac{14 + 4 \sqrt{6} - 12 \sqrt{2} - 24 \sqrt{3} }{- 10} [/tex] =
= [tex]- \frac{2 ( 7 + 2 \sqrt{6} - 6 \sqrt{2} - 12 \sqrt{3} )}{10} [/tex] =
[ Simplificam 10 cu 2.]
= [tex] -\frac{7 + 2 \sqrt{6} - 6 \sqrt{2} - 12 \sqrt{3} }{5} [/tex].
