Question

Racionalize o denominador da fração 3/4V2-2V3

Answer 1

$\dfrac{3}{4 \sqrt{2}-2 \sqrt{3}} \\ \\ \\ \\ \dfrac{3.(4 \sqrt{2}+2 \sqrt{3})}{(4 \sqrt{2}-2 \sqrt{3}).(4 \sqrt{2}+2 \sqrt{3})} \\ \\ \\\dfrac{12.\sqrt{2}+6 \sqrt{3}}{4.4.( \sqrt{2})^2 + 4.2 \sqrt{2} .\sqrt{3} - 2 .4\sqrt{2} \sqrt{3} -2.2 (\sqrt{3})^2}} \\ \\ \\ \dfrac{6.(2\sqrt{2}+ \sqrt{3}) }{32+ 8 \sqrt{6} - 8 \sqrt{6} - 12} \\ \\ \\ \dfrac{6.(2\sqrt{2}+ \sqrt{3}) }{32 - 12 } \\ \\ \\ \dfrac{6.(2\sqrt{2}+ \sqrt{3}) }{20} \\ \\ \\ =\ \textgreater \ \dfrac{3.(2\sqrt{2}+ \sqrt{3}) }{10}$