Question

Simplify 3√2÷√6-√3-4√3÷√6+√2

Answer 1

$3 \sqrt{2} \div ( \sqrt{6} - \sqrt{3} ) - 4 \sqrt{3} \div ( \sqrt{6} + \sqrt{2} ) \\ = 3 \sqrt{2} \times ( \sqrt{6} + \sqrt{3} ) \div ( \sqrt{6} - \sqrt{3} ) \times ( \sqrt{6} + \sqrt{3} ) - 4 \sqrt{3} \times ( \sqrt{6} - \sqrt{2} ) \div ( \sqrt{6} + \sqrt{2} ) \times ( \sqrt{6} - \sqrt{2} ) \\ = 3 \times 2 \times \sqrt{3} + 3 \sqrt{6} \div (6 - 3) - 4 \times 3 \times \sqrt{2} + 4 \sqrt{6} \div (6 - 2) \\ = 3(2 \sqrt{3} + \sqrt{6} ) \div 3 - 4(3 \sqrt{2} - \sqrt{6} )\div 4 \\ = 2 \sqrt{3} + \sqrt{6} - 3 \sqrt{2} + \sqrt{6} \\ = 2 \sqrt{3} - 3 \sqrt{2} + 2 \sqrt{6}$
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