Question

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

Answer 1

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