Răspuns:
Florin
Explicație pas cu pas:
[tex]a = [ \frac{2}{ \sqrt{6} } + \frac{3 \sqrt{2} }{2 \sqrt{3} } - ( \frac{8 \sqrt{2} }{ \sqrt{27} } + \frac{2 \sqrt{3} }{ \sqrt{18} } )] \times ( - \frac{12}{7 \sqrt{6} } ) = [ \frac{2}{ \sqrt{6} } + \frac{3 \sqrt{2} }{2 \sqrt{3} } - ( \frac{8 \sqrt{2} }{ 3\sqrt{3} } + \frac{2 \sqrt{3} }{ 3\sqrt{2} } )] \times ( - \frac{12}{7 \sqrt{6} } ) = [ \frac{2 \times 6}{\sqrt{6} \times 6} + \frac{3 \sqrt{2}\times3\sqrt{2} }{2 \sqrt{3} \times 3\sqrt{2}}-(\frac{8 \sqrt{2} \times 2\sqrt{2} }{ 3\sqrt{3} \times 2\sqrt{2}} + \frac{2 \sqrt{3} \times 2\sqrt{3}}{ 3\sqrt{2} \times 2\sqrt{3}})] \times (-\frac{12}{7 \sqrt{6}}) = [ \frac{12}{6\sqrt{6}} + \frac{18}{6 \sqrt{6}}-(\frac{32}{ 6\sqrt{6}} + \frac{12}{ 6\sqrt{6}})] \times (-\frac{12}{7 \sqrt{6}}) = ( \frac{12 + 18}{6\sqrt{6}} - \frac{32 + 12}{ 6\sqrt{6}}) \times (-\frac{12}{7 \sqrt{6}}) = ( \frac{30}{6\sqrt{6}} - \frac{44}{ 6\sqrt{6}}) \times (-\frac{12}{7 \sqrt{6}}) = \frac{30 - 44}{6\sqrt{6}} \times (-\frac{12}{7 \sqrt{6}}) = - \frac{14}{6 \sqrt{6} } \times ( - \frac{12}{7 \sqrt{6}}) = \frac{14 \times 12}{6 \sqrt{6} \times 7 \sqrt{6} } = \frac{2 \times 2}{6} = \frac{2}{3}[/tex]
