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

Sagot :

konrad509
[tex]\dfrac{2\sqrt3-\sqrt6}{3\sqrt6+2\sqrt3}=\\ \dfrac{(2\sqrt3-\sqrt6)(3\sqrt6-2\sqrt3)}{(3\sqrt6+2\sqrt3)(3\sqrt6-2\sqrt3)}=\\ \dfrac{6\sqrt{18}-12-18+2\sqrt{18}}{54-12}=\\ \dfrac{-30+8\sqrt{18}}{42}=\\ \dfrac{-30+24\sqrt{2}}{42}=\\ \dfrac{-5+4\sqrt{2}}{7} [/tex]
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