Question

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Answer 1

$\frac{2}{ \sqrt{3} - 1 } - \sqrt{3} = \\ \\ \frac{2}{ \sqrt{3} - 1 } \times \frac{ \sqrt{3} + 1 }{ \sqrt{3} + 1 } - \sqrt{3} = \\ \\ \frac{2( \sqrt{3} + 1) }{( \sqrt{3} - 1)( \sqrt{3} + 1) } - \sqrt{3} = \\ \\ \frac{2( \sqrt{3} + 1) }{ \sqrt{3} ^{2} - {1}^{2} } - \sqrt{3} = \\ \\ \frac{2( \sqrt{3} + 1) }{3 - 1} - \sqrt{3} = \\ \\ \frac{2( \sqrt{3} + 1) }{2} - \sqrt{3} = \\ \\ \sqrt{3} + 1 - \sqrt{3} = \\ \\ ( \sqrt{3} - \sqrt{3}) + 1 = \\ \\ 1 \: \: (Adevarat)$

Answer 2

Amplific fractia cu conjugata, √3+1.

2(√3+1)/(√3+1)(√3-1)-√3=1

2(√3+1)/(√3²-1²)-√3=1

2(√3+1)(3-1)-√3=1

2(√3+1)/2-√3=1

2 de la numarator se simplifica cu 2 de la numitor

√3+1-√3=1

1=1 (adevarat)