Question

rapid va roggfgggg!!!!! exercițiul e in atașament​

Answer 1

Explicație pas cu pas:

a)

$\dfrac{12}{ \sqrt{3} } + \dfrac{15}{5 \sqrt{3} } - \dfrac{21}{7 \sqrt{3} } + \dfrac{18}{ \sqrt{3} } = \dfrac{12}{ \sqrt{3} } + \dfrac{3}{\sqrt{3} } - \dfrac{3}{\sqrt{3} } + \dfrac{18}{ \sqrt{3} } = \dfrac{12 + 3 - 3 + 18}{ \sqrt{3} } = \dfrac{30}{ \sqrt{3} } = \dfrac{30 \sqrt{3} }{3} = 10 \sqrt{3}$

b)

$\dfrac{8}{ 3\sqrt{2} } - \dfrac{8}{2 \sqrt{2} } + \dfrac{8}{6 \sqrt{2} } - \dfrac{8}{12 \sqrt{2} } = \dfrac{8}{ 3\sqrt{2} } - \dfrac{^{3)}4}{\sqrt{2} } + \dfrac{4}{3 \sqrt{2} } - \dfrac{2}{3 \sqrt{2} } = \dfrac{8 - 12 + 4 - 2}{3 \sqrt{2} } = - \dfrac{2}{3 \sqrt{2} } = - \dfrac{2 \sqrt{2} }{3 \cdot 2} = - \dfrac{ \sqrt{2} }{3}$

c)

$\dfrac{^{2)} 24}{5\sqrt{6} } - \dfrac{^{10)}12}{ \sqrt{6} } + \dfrac{21}{10\sqrt{6} } - \dfrac{^{5)}28}{2\sqrt{6} } = \dfrac{48 - 120 + 21 - 140}{10\sqrt{6} } = - \dfrac{191}{10\sqrt{6} } = - \dfrac{191 \sqrt{6} }{60}$

d)

$\dfrac{^{15)} 7}{2\sqrt{5} } + \dfrac{^{10)}7}{3\sqrt{5} } - \dfrac{^{5)}7}{6\sqrt{5} } + \dfrac{^{6)}7}{5\sqrt{5} } = \dfrac{7 \cdot (15 + 10 - 5 + 6)}{30\sqrt{5} } = \dfrac{7 \cdot 26}{30\sqrt{5} } = \dfrac{91}{15\sqrt{5} } = \dfrac{91 \sqrt{5} }{75}$