Question

$\frac{1}{5\sqrt{3}-10 } - \frac{1}{5\sqrt{3}+10 }$

Answer 1

$\frac{1}{5 \sqrt{3} - 10 } - \frac{1}{5 \sqrt{3} + 10 } = \frac{1}{5} ( \frac{1}{ \sqrt{3} - 2} - \frac{1}{ \sqrt{3} + 2} ) = \frac{1}{5} ( \frac{ \sqrt{3} + 2 - ( \sqrt{3} - 2) }{( \sqrt{3} - 2)( \sqrt{3} + 2) } ) = \frac{1}{5} \times \frac{4}{( \sqrt{3} ) {}^{2} - 2 {}^{2} } = \frac{4}{5(3 - 4)} = \frac{4}{ - 5} = - \frac{4}{5} = - 0.8$

Ответ: -0.8