Question

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Answer 1

8/3√3+5

Răspuns:

Bună,

$\frac{24}{ \sqrt{3} } + \frac{30}{5 \sqrt{3} } - \frac{42}{7 \sqrt{3} } + \frac{36}{ \sqrt{3} } = \\ \frac{24 \sqrt{3} }{3} + \frac{30 \sqrt{3} }{15} - \frac{42 \sqrt{3} }{21} + \frac{36 \sqrt{3} }{3} = \\ 8 \sqrt{3} + 2 \sqrt{3} - 2 \sqrt{3} + 12 \sqrt{3} = \\ 20 \sqrt{3}$

$\frac{16}{2 - \sqrt{3} } + \frac{12}{ \sqrt{3} + 1} - \frac{6}{2 \sqrt{3} - 3 } - \frac{8}{3 \sqrt{3} + 5 } = \\ \frac{16(2 + \sqrt{3}) }{4 - 3} + \frac{12( \sqrt{3} - 1) }{3 - 1} - \frac{6(2 \sqrt{3} + 3)}{4 \times 3 - 9} - \frac{8(3 \sqrt{3} - 5 )}{9 \times 3 - 25} = \\ 16(2 + \sqrt{3} ) + \frac{12( \sqrt{3} - 1) }{2} - \frac{6(2 \sqrt{3} + 3) }{3} - \frac{8(3 \sqrt{3} - 5) }{2} = \\ 32 + 16\sqrt{3} + 6( \sqrt{3} - 1) - 2(2 \sqrt{3} + 3) - 4(3 \sqrt{3} - 5) = \\ 32 + 16 \sqrt{3} + 6 \sqrt{3} - 6 - 4 \sqrt{3} - 6 - 12 \sqrt{3} + 20 = 40 + 6 \sqrt{3}$

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Answer 2

8/3√3+5

Răspuns:

Bună,

$\frac{24}{ \sqrt{3} } + \frac{30}{5 \sqrt{3} } - \frac{42}{7 \sqrt{3} } + \frac{36}{ \sqrt{3} } = \\ \frac{24 \sqrt{3} }{3} + \frac{30 \sqrt{3} }{15} - \frac{42 \sqrt{3} }{21} + \frac{36 \sqrt{3} }{3} = \\ 8 \sqrt{3} + 2 \sqrt{3} - 2 \sqrt{3} + 12 \sqrt{3} = \\ 20 \sqrt{3}$

$\frac{16}{2 - \sqrt{3} } + \frac{12}{ \sqrt{3} + 1} - \frac{6}{2 \sqrt{3} - 3 } - \frac{8}{3 \sqrt{3} + 5 } = \\ \frac{16(2 + \sqrt{3}) }{4 - 3} + \frac{12( \sqrt{3} - 1) }{3 - 1} - \frac{6(2 \sqrt{3} + 3)}{4 \times 3 - 9} - \frac{8(3 \sqrt{3} - 5 )}{9 \times 3 - 25} = \\ 16(2 + \sqrt{3} ) + \frac{12( \sqrt{3} - 1) }{2} - \frac{6(2 \sqrt{3} + 3) }{3} - \frac{8(3 \sqrt{3} - 5) }{2} = \\ 32 + 16\sqrt{3} + 6( \sqrt{3} - 1) - 2(2 \sqrt{3} + 3) - 4(3 \sqrt{3} - 5) = \\ 32 + 16 \sqrt{3} + 6 \sqrt{3} - 6 - 4 \sqrt{3} - 6 - 12 \sqrt{3} + 20 = 40 + 6 \sqrt{3}$

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