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Simplify completely: 2 square root 3 - square root 6 all over 3 square root 6 + 2 square root 3

Simplify completely: 2 square root 3 - square root 6 all over 3 square root 6 + 2 square root 3
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5 votes
Simplify completely: 2 square root 3 - square root 6 all over 3 square root 6 + 2 square root 3

User Benjamin Muschko
by
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1 Answer

5 votes

(2\sqrt3-\sqrt6)/(3\sqrt6+2\sqrt3)=\\ ((2\sqrt3-\sqrt6)(3\sqrt6-2\sqrt3))/((3\sqrt6+2\sqrt3)(3\sqrt6-2\sqrt3))=\\ (6√(18)-12-18+2√(18))/(54-12)=\\ (-30+8√(18))/(42)=\\ (-30+24√(2))/(42)=\\ (-5+4√(2))/(7)
User Chrispytoes
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8.6k points
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