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Rationalise... please explain the answer step by step..

Dear Student ,

\frac{4 \sqrt{3} + 5 \sqrt{2}}{\sqrt{48} + \sqrt{18}} = \frac{4 \sqrt{3} + 5 \sqrt{2}}{4 \sqrt{3} + 3 \sqrt{2}} = \frac{4 \sqrt{3} + 5 \sqrt{2}}{4 \sqrt{3} + 3 \sqrt{2}} \times \frac{4 \sqrt{3} - 3 \sqrt{2}}{4 \sqrt{3} - 3 \sqrt{2}} = \frac{{(4 \sqrt{3})}^{2} - (4 \sqrt{3}) (3 \sqrt{2}) + (5 \sqrt{2}) (4 \sqrt{3}) - (5 \sqrt{2}) (3 \sqrt{2})}{{(4 \sqrt{3})}^{2} - {(3 \sqrt{2})}^{2}} = \frac{48 - 12 \sqrt{6} + 20 \sqrt{6} - 30}{48 - 18} = \frac{18 + 8 \sqrt{6}}{30} = \frac{9 + 4 \sqrt{6}}{15} ANS . . .

Regards!

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