Question

Va rog ajutați-mă la exercițiul acesta!!

Answer 1

Vom raționaliza numitorii:

$\frac{3}{ \sqrt{2} } \div \frac{2}{ \sqrt{6} } + \frac{5}{2 \sqrt{3} } = \\ = \frac{3 \sqrt{2} }{2} \div \frac{2 \sqrt{6} }{6} + \frac{5 \sqrt{3} }{6} \\ = \frac{3 \sqrt{2} }{2} \times \frac{6}{2 \sqrt{6} } + \frac{5 \sqrt{3} }{6} \\ = \frac{18 \sqrt{2} }{4 \sqrt{6}}+ \frac{5 \sqrt{3} }{6} \\ = \frac{9 \sqrt{2} }{2 \sqrt{6} } + \frac{5 \sqrt{3} }{6} \\ = \frac{9 \sqrt{12} }{12} + \frac{5 \sqrt{3} }{6} \\ = \frac{9 \sqrt{12 } + 10 \sqrt{3} }{12} .$