Question

$\frac{ \sqrt{15} - \sqrt{6} }{5- \sqrt{10} }$
Сократить дробь.

Answer 1

$\frac{ \sqrt{15}- \sqrt{6} }{5- \sqrt{10} }= \frac{ \sqrt{5}* \sqrt{3}- \sqrt{2}* \sqrt{3} }{ \sqrt{5}* \sqrt{5}- \sqrt{2}* \sqrt{5} }= \frac{ \sqrt{3}( \sqrt{5}- \sqrt{2} ) }{ \sqrt{5}( \sqrt{5}- \sqrt{2} ) }= \frac{ \sqrt{3} }{ \sqrt{5} }* \frac{ \sqrt{5} }{ \sqrt{5} }= \frac{ \sqrt{15} }{5}$

Answer 2

$\frac{ \sqrt{15} - \sqrt{6} }{5- \sqrt{10} } = \frac{ \sqrt{3} * \sqrt{5} - \sqrt{2} * \sqrt{3} }{ \sqrt{5} * \sqrt{5} - \sqrt{2} * \sqrt{5} } = \frac{ \sqrt{3} *( \sqrt{5} - \sqrt{2} )}{ \sqrt{5} *( \sqrt{5} - \sqrt{2} )} = \frac{ \sqrt{3} }{5}$