Question

\(\dfrac{1}{2\sqrt{2}-3\sqrt{3}}\)

Answer 1

\(\dfrac{1}{2\sqrt{2}-3\sqrt{3}}=\dfrac{2\sqrt{2}+3\sqrt{3}}{8-27}\)

\(=\dfrac{-2\sqrt{2}-3\sqrt{3}}{19}\)

Answer 2

\(\dfrac{1}{2\sqrt{2}-3\sqrt{3}}\)

\(=\dfrac{2\sqrt{2}+3\sqrt{3}}{\left(2\sqrt{2}-3\sqrt{3}\right)\left(2\sqrt{2}+3\sqrt{3}\right)}\)

\(=\dfrac{2\sqrt{2}+3\sqrt{3}}{\left(2\sqrt{2}\right)^2-\left(3\sqrt{3}\right)^2}\)

\(=\dfrac{2\sqrt{2}+3\sqrt{3}}{8-27}\)

\(=-\dfrac{2\sqrt{2}+3\sqrt{3}}{19}\)