Răspuns:
Bună,
[tex] \frac{4}{ \sqrt{6} - 2 } = \\ \frac{4( \sqrt{6} + 2) }{6 - 4} = \\ \frac{4( \sqrt{6} - 2) }{2} = \\ 2( \sqrt{6} - 2) = \\ 2 \sqrt{6} - 4 [/tex]
[tex] \frac{ \sqrt{ 6} + \sqrt{5} }{ \sqrt{6} - \sqrt{5} } = \\ \frac{( \sqrt{6} + \sqrt{5}) \times ( \sqrt{6} + \sqrt{5} ) }{6 - 5} = \\ (6 + \sqrt{5} ) ^{2} = \\ ( \sqrt{6}) ^{2} + 2 \times \sqrt{6} \times \sqrt{5} + ( \sqrt{5} ) ^{2} = \\ 6 + 2 \sqrt{30} + 5 = \\ 11 + \sqrt{30} [/tex]
[tex] \frac{1}{3 \sqrt{2} - 2 \sqrt{5} } = \\ \frac{3 \sqrt{2} + 2 \sqrt{5} }{9 \times 2 - 4 \times 5} = \\ \frac{3 \sqrt{2} + 2 \sqrt{5} }{ - 2} = \\ - \frac{3 \sqrt{2 }+ 2 \sqrt{5} }{2} [/tex]
[tex] \frac{ \sqrt{30} - \sqrt{18} }{10 - 2 \sqrt{15} } = \\ \frac{ \sqrt{30 } - 3 \sqrt{2} }{10 - 2 \sqrt{15} } = \\ \frac{( \sqrt{30} - 3 \sqrt{2} ) \times (10 + 2 \sqrt{15)} }{100 - 4 \times 15} = \\ \frac{ 10\sqrt{30} + 30 \sqrt{2} - 30 \sqrt{2} - 6 \sqrt{30} }{100 - 60} = \\ \frac{4 \sqrt{30} }{40} = \\ \frac{ \sqrt{30} }{10} [/tex]
Sper că te-am ajutat
