Question

вычислить

 

$<var>(\frac{15}{\sqrt{6}+1}+ \frac{4}{\sqrt{6}-2}- \frac{12}{3-\sqrt{6}})\cdot(\sqrt{6}+11)</var>$

 

Answer 1

$<var>(\frac{15}{\sqrt{6}+1}+ \frac{4}{\sqrt{6}-2}- \frac{12}{3-\sqrt{6}})\cdot(\sqrt{6}+11)=\\ =(\frac{15(\sqrt{6}-2)(3-\sqrt{6})+4(\sqrt{6}+1)(3-\sqrt{6})-12(\sqrt{6}+1)(\sqrt{6}-2)}{(\sqrt{6}+1)(\sqrt{6}-2)(3-\sqrt{6})})\cdot(\sqrt{6}+11)=\\ =(\frac{15(5\sqrt{6}-12)+4(2\sqrt{6}-3)-12(4-\sqrt{6})}{18-7\sqrt6})\cdot(\sqrt{6}+11)=\\ =(\frac{75\sqrt{6}-180+8\sqrt{6}-12-48+12\sqrt{6})}{18-7\sqrt6})\cdot(\sqrt{6}+11)=\\ =(\frac{95\sqrt{6}-240}{18-7\sqrt6})\cdot(\sqrt{6}+11)=\\ </var>$

$<var>=\frac{(95\sqrt{6}-240)(\sqrt{6}+11)}{18-7\sqrt6}=\frac{5(19\sqrt{6}-48)(\sqrt{6}+11)}{18-7\sqrt6}=\\ =\frac{5(114+209\sqrt6-48\sqrt6-528)}{18-7\sqrt6}=\frac{5(161\sqrt6-414)}{18-7\sqrt6}=\frac{5*23(7\sqrt6-18)}{18-7\sqrt6}=\\ =\frac{115(7\sqrt6-18)}{-(7\sqrt6-18)}=-115 </var>$