Respuesta :
Answer:
[tex]\boxed{\bold{\frac{6\sqrt{6}+6\sqrt{2}+6\sqrt{3}+6}{5\sqrt{6}+4+12\sqrt{3}-3\sqrt{2}}}}[/tex]
Step By Step Explanation:
Remove Parenthesis: (a) = a
[tex]\bold{\frac{\sqrt{6}}{\sqrt{2}+\sqrt{3}+\frac{2\sqrt{2}}{\sqrt{6}+\sqrt{3}}-\frac{4\sqrt{3}}{\sqrt{6}+\sqrt{2}}}}[/tex]
Join [tex]\bold{\sqrt{2}+\sqrt{3}+\frac{2\sqrt{2}}{\sqrt{6}+\sqrt{3}}-\frac{4\sqrt{3}}{\sqrt{6}+\sqrt{2}}: \ \frac{5\sqrt{6}+4+12\sqrt{3}-3\sqrt{2}}{6+2\sqrt{3}+3\sqrt{2}+\sqrt{6}}}[/tex]
[tex]\bold{\frac{\sqrt{6}}{\frac{5\sqrt{6}+4+12\sqrt{3}-3\sqrt{2}}{6+2\sqrt{3}+3\sqrt{2}+\sqrt{6}}}}[/tex]
Apply Fraction Rule: [tex]\bold{\frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}}[/tex]
[tex]\bold{\frac{\sqrt{6}\left(6+2\sqrt{3}+3\sqrt{2}+\sqrt{6}\right)}{5\sqrt{6}+4+12\sqrt{3}-3\sqrt{2}}}[/tex]
Expand [tex]\bold{\frac{\sqrt{6}\left(6+2\sqrt{3}+3\sqrt{2}+\sqrt{6}\right)}{5\sqrt{6}+4+12\sqrt{3}-3\sqrt{2}}: \ \frac{6\sqrt{6}+6\sqrt{2}+6\sqrt{3}+6}{5\sqrt{6}+4+12\sqrt{3}-3\sqrt{2}}}[/tex]
[tex]\bold{\frac{6\sqrt{6}+6\sqrt{2}+6\sqrt{3}+6}{5\sqrt{6}+4+12\sqrt{3}-3\sqrt{2}}}[/tex]
- Mordancy
