Question

* Racionalizar
* 5/12√3



* 13/√2 - √7

Answer 1

$\frac{5}{12 \sqrt{3}}* \frac{ \sqrt{3}}{ \sqrt{3}} = \frac{5* \sqrt{3}}{12 \sqrt{3}* \sqrt{3}} \\ \\ \frac{5}{12 \sqrt{3}}* \frac{ \sqrt{3}}{ \sqrt{3}} = \frac{5* \sqrt{3}}{12 *3\sqrt{3}^2} \\ \\ \frac{5}{12 \sqrt{3}}* \frac{ \sqrt{3}}{ \sqrt{3}} = \frac{5* \sqrt{3}}{12 *3} \\ \\ \frac{5}{12 \sqrt{3}}* \frac{ \sqrt{3}}{ \sqrt{3}} = \frac{5* \sqrt{3}}{36}= \boxed{ \frac{5}{36} \sqrt{3}}$

$\frac{13}{ \sqrt{2}- \sqrt{7} }* \frac{ \sqrt{2}+ \sqrt{7}}{ \sqrt{2} + \sqrt{7}} = \\ \\ \frac{13}{ \sqrt{2}- \sqrt{7} }= \frac{13*( \sqrt{2}+ \sqrt{7})}{ (\sqrt{2})^2- \sqrt{14}+ \sqrt{14} -( \sqrt{7})^2} \\ \\ \frac{13}{ \sqrt{2}- \sqrt{7} }= \frac{13 \sqrt{2}+13\sqrt{7}}{ (\sqrt{2})^2 -( \sqrt{7})^2} \\ \\ \frac{13}{ \sqrt{2}- \sqrt{7} }= \frac{13 \sqrt{2}+13\sqrt{7}}{ 2-7} \\ \\ \frac{13}{ \sqrt{2}- \sqrt{7} }= \frac{13 \sqrt{2}+13\sqrt{7}}{ -5}$

$\frac{13}{ \sqrt{2}- \sqrt{7} }= \boxed{- \frac{13}{5} \sqrt{2}- \frac{13}{5} \sqrt{7} }$

Espero que te sirva, salu2!!!!