Question

dau coroana$\frac{4 - 3 \sqrt{6} }{2 \sqrt{3} } - \frac{5 \sqrt{6 } - 7}{4 \sqrt{2} } + \frac{3 + 2 \sqrt{6} }{5 \sqrt{3} } - \frac{4 \sqrt{6} - 3}{6 \sqrt{2} } =$
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Answer 1

Răspuns:

Explicație pas cu pas:

$\frac{4-3\sqrt{6} }{2\sqrt{3} } -\frac{5\sqrt{6} -7}{4\sqrt{2} } +\frac{3+2\sqrt{6} }{5\sqrt{3} } -\frac{4\sqrt{6} -3}{6\sqrt{2} } =\\ \frac{(4-3\sqrt{6})\sqrt{3}  }{6} -\frac{(5\sqrt{6}-7)\sqrt{2}  }{8} +\frac{(3+2\sqrt{6} )\sqrt{3} }{15} -\frac{(4\sqrt{6}-3)\sqrt{2}  }{12} =$$\\  \frac{(4-3\sqrt{6})20\sqrt{3}  }{120} -\frac{(5\sqrt{6}-7)15\sqrt{2}  }{120} +\frac{(3+2\sqrt{6} )8\sqrt{3} }{120} -\frac{(4\sqrt{6}-3)10\sqrt{2}  }{120} =\\  \frac{80\sqrt{3}-60\sqrt{18} -75\sqrt{12} +105\sqrt{2} +24\sqrt{3} +16\sqrt{18} -40\sqrt{12} +30\sqrt{2}  }{120} =\\ \frac{80\sqrt{3}  -180\sqrt{2}-150\sqrt{3} +105\sqrt{2} +24\sqrt{3}+48\sqrt{2} -80\sqrt{3} +30\sqrt{2}  }{120} =\\ \frac{3\sqrt{2}-126\sqrt{3}  }{120} =\\ \frac{\sqrt{2}-42\sqrt{3}  }{40}$