Answer:
[tex] \longmapsto4 \sqrt{3} + 3 \sqrt{2} .[/tex]
Step-by-step explanation:
[tex]\sf{\dfrac{30}{4\sqrt{3} - \sqrt{18}}}[/tex]
By rationalizing the denominator:-
[tex] = \sf{\dfrac{30}{4\sqrt{3} - \sqrt{18}} \times \dfrac{4\sqrt{3} + \sqrt{18}}{4\sqrt{3} + \sqrt{18}}}[/tex]
[tex] = \sf{\dfrac{30(4\sqrt{3} + \sqrt{18})}{(4\sqrt{3})^2 - (\sqrt{18})^2}}[/tex]
[tex] = \sf{\dfrac{30(4\sqrt{3} + \sqrt{18})}{48 - 18}}[/tex]
[tex] = \sf{\dfrac{30(4\sqrt{3} + \sqrt{18})}{30}}[/tex]
[tex] = \sf{\dfrac{\not{30}(4\sqrt{3} + \sqrt{18})}{\not{30}}}[/tex]
[tex] = \sf{4\sqrt{3} + 3\sqrt{2}}[/tex]
[tex] \therefore \sf{\dfrac{30}{4\sqrt{3} - \sqrt{18}} = 4\sqrt{3} + 3\sqrt{2}}[/tex]
