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Sliva [168]
3 years ago
12

((√6) ÷ (√2+√3) + ((2√2)÷(√6+√3)) - ((4√3)÷(√6+√2))

Mathematics
1 answer:
DiKsa [7]3 years ago
4 0

Answer:

\boxed{\bold{\frac{6\sqrt{6}+6\sqrt{2}+6\sqrt{3}+6}{5\sqrt{6}+4+12\sqrt{3}-3\sqrt{2}}}}

Step By Step Explanation:

Remove Parenthesis: (a) = a

\bold{\frac{\sqrt{6}}{\sqrt{2}+\sqrt{3}+\frac{2\sqrt{2}}{\sqrt{6}+\sqrt{3}}-\frac{4\sqrt{3}}{\sqrt{6}+\sqrt{2}}}}

Join \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}}}

\bold{\frac{\sqrt{6}}{\frac{5\sqrt{6}+4+12\sqrt{3}-3\sqrt{2}}{6+2\sqrt{3}+3\sqrt{2}+\sqrt{6}}}}

Apply Fraction Rule: \bold{\frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}}

\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}}}

Expand \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}}}

\bold{\frac{6\sqrt{6}+6\sqrt{2}+6\sqrt{3}+6}{5\sqrt{6}+4+12\sqrt{3}-3\sqrt{2}}}

- Mordancy

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