1 Rationalize the denominator: \frac{3\sqrt{2}}{\sqrt{6}-\sqrt{3}}(\frac{\sqrt{6}+\sqrt{3}}{\sqrt{6}+\sqrt{3}})√6−√33√2(√6+√3√6+√3)
\frac{6\sqrt{3}+3\sqrt{6}}{{\sqrt{6}}^{2}-{\sqrt{3}}^{2}}-\frac{3}{3-\sqrt{6}}√62−√326√3+3√6−3−√63
2 Factor out the common term 33
\frac{3(2\sqrt{3}+\sqrt{6})}{{\sqrt{6}}^{2}-{\sqrt{3}}^{2}}-\frac{3}{3-\sqrt{6}}√62−√323(2√3+√6)−3−√63
3 Use this rule: {\sqrt{x}}^{2}=x√x2=x
\frac{3(2\sqrt{3}+\sqrt{6})}{6-{\sqrt{3}}^{2}}-\frac{3}{3-\sqrt{6}}6−√323(2√3+√6)−3−√63
4 Use this rule: {\sqrt{x}}^{2}=x√x2=x
\frac{3(2\sqrt{3}+\sqrt{6})}{6-3}-\frac{3}{3-\sqrt{6}}6−33(2√3+√6)−3−√63
5 Simplify 6-36−3 to 33
\frac{3(2\sqrt{3}+\sqrt{6})}{3}-\frac{3}{3-\sqrt{6}}33(2√3+√6)−3−√63
6 Cancel 33
2\sqrt{3}+\sqrt{6}-\frac{3}{3-\sqrt{6}}2√3+√6−3−√63
7 Rationalize the denominator: \frac{3}{3-\sqrt{6}}(\frac{3+\sqrt{6}}{3+\sqrt{6}})3−√63(3+√63+√6)