Question

Сократите дробь:
1)$frac{a -sqrt{3a} +3}{a sqrt{a}+3 sqrt{3} }$.
2)$frac{2 sqrt{10}-5 }{4- sqrt{10} }$.
3)$frac{9-2 sqrt{3} }{3 sqrt{6}-2 sqrt{2} }$.

Answer 1

$frac{a -sqrt{3a} +3}{a sqrt{a}+3 sqrt{3} } = frac{a -sqrt{3a} +3}{ (sqrt{a}+ sqrt{3} )(a -sqrt{3a} +3)} = frac{1}{ sqrt{a}+ sqrt{3}} \ frac{2 sqrt{10}-5 }{4- sqrt{10} } = frac{sqrt{10}(2 -0,5sqrt{10}) }{sqrt{10}(0,4sqrt{10}-1)} = frac{2 -0,5sqrt{10} }{0,4sqrt{10}-1} \ frac{9-2 sqrt{3} }{3 sqrt{6}-2 sqrt{2} } = frac{ sqrt{3}(3 sqrt{3}-2) }{ sqrt{2} (3 sqrt{3} -2) } = frac{ sqrt{3}}{ sqrt{2} } = sqrt{1,5}$