Question

Сократить дробь. Помогите, пожалуйста.

$frac{8 x^{2}-x }{6x}$

$frac{17+2 sqrt{30} }{ sqrt{15}+ sqrt{2} }$

Answer 1

$frac{8x^2-x}{6x}=frac{x(8x-1)}{6x}=frac{8x-1}{6}\\frac{17+2sqrt{30}}{sqrt{15}+sqrt2}=frac{(17+2sqrt{30})(sqrt{15}-sqrt2)}{(sqrt{15}+sqrt2)(sqrt{15}-sqrt2)}=frac{17sqrt{15}-17sqrt2+2sqrt{30cdot 15}-2sqrt{30cdot 2}}{15-2}=\\=frac{17sqrt{15}-17sqrt{2}+30sqrt2-4sqrt{15}}{13}=$

$=frac{13sqrt{15}+13sqrt2}{13}=sqrt{15}+sqrt2$