Analizam fiecare modul:
[tex]3\sqrt2-2\sqrt3\ \textgreater \ 0 \Longrightarrow |3\sqrt2-2\sqrt3| = 3\sqrt2-2\sqrt3[/tex]
[tex]4\sqrt2-3\sqrt3 \ \textgreater \ 0 \Longrightarrow |4\sqrt2-3\sqrt3 | = 4\sqrt2-3\sqrt3[/tex]
[tex]\sqrt2-2\sqrt3\ \textless \ 0 \Longrightarrow |\sqrt2-2\sqrt3|= 2\sqrt3 -\sqrt2[/tex]
Expresia data devine:
[tex](\dfrac{3\sqrt2-2\sqrt3}{4} - \dfrac{4\sqrt2-3\sqrt3}{6} + \dfrac{2\sqrt3-\sqrt2}{12}):(\dfrac{\sqrt3}{2})^3[/tex]
Aducem la acelasi numitor in prima paranteza, numitorul comun este 12.
Se amplifica prima fractie cu 3, iar a doua cu 2 si obtinem :
[tex]\left(\dfrac{9\sqrt2-6\sqrt3-8\sqrt2+6\sqrt3+2\sqrt3-\sqrt2}{12}\right) : \\\;\\
\dfrac{\sqrt3\cdot\sqrt3\cdot\sqrt3}{8} = \dfrac{2\sqrt3}{12}\cdot\dfrac{8}{3\sqrt3} \\\;\\
= \dfrac{4}{9}[/tex]
