Question

14. Efectuati calculele:
$( \frac { 2 \sqrt { 6 } } { 3 } - \frac { 3 } { 2 \sqrt { 6 } } ) + ( \frac { 3 \sqrt { 6 } } { 2 } - \frac { 2 } { 3 \sqrt { 6 } } ) + ( \frac { 6 } { 2 \sqrt { 6 } } - \frac { 6 } { 3 \sqrt { 6 } } )$
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Answer 1

$\it = (\dfrac{2\sqrt6}{3}+\dfrac{3\sqrt6}{2})+(\dfrac{6}{2\sqrt6}-\dfrac{3}{2\sqrt6})-(\dfrac{6}{3\sqrt6}+\dfrac{2}{3\sqrt6})=\dfrac{13\sqrt6}{6}+\dfrac{3}{2\sqrt6}-\dfrac{8}{3\sqrt6}=\\ \\ \\ =\dfrac{^{6)}13\sqrt6}{6}+\dfrac{^{3)}3\sqrt6}{12}-\dfrac{^{2)}8\sqrt6}{18}=\dfrac{71\sqrt6}{36}$

Answer 2

Răspuns:

$\frac{2 \sqrt{6} }{3} - \frac{3}{2 \sqrt{6} } + \frac{3 \sqrt{6} }{2} - \frac{2}{3 \sqrt{6} } + ( \frac{3}{ \sqrt{6} } - \frac{2}{ \sqrt{6} } ) \\ \\ = \frac{2 \sqrt{6} }{3} - \frac{ \sqrt{6} }{4} + \frac{3 \sqrt{6} }{2} - \frac{ \sqrt{6} }{9} + \frac{1}{ \sqrt{6} } \\ \\ = \frac{2 \sqrt{6} }{3} - \frac{ \sqrt{6} }{4} + \frac{3 \sqrt{6} }{2} - \frac{ \sqrt{6} }{9} + \frac{ \sqrt{6} }{6} \\ \\ = \frac{12 \times 2 \sqrt{6} }{12 \times 3} - \frac{9 \sqrt{6} }{9 \times 4} + \frac{18 \times 3 \sqrt{6} }{18 \times 2} - \frac{4 \sqrt{6} }{4 \times 9} + \frac{6 \sqrt{6} }{6 \times 6} \\ \\ = \frac{24 \sqrt{6 } - 9 \sqrt{6} + 54 \sqrt{6} - 4 \sqrt{6} + 6 \sqrt{6} }{36 } \\ \\ = \bf\blue{\boxed{ \frac{71 \sqrt{6} }{36} }}$