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(D) Given expression: $\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$Simplify the denominator: $\sqrt{48} = \sqrt{16 	imes 3} = 4 \sqrt{3}$ and $

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$\frac{9+4 \sqrt{6}}{15}$

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(D) Given expression: $\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$Simplify the denominator: $\sqrt{48} = \sqrt{16 	imes 3} = 4 \sqrt{3}$ and $\sqrt{18} = \sqrt{9 	imes 2} = 3 \sqrt{2}$.So,the expression becomes: $\frac{4 \sqrt{3}+5 \sqrt{2}}{4 \sqrt{3}+3 \sqrt{2}}$.To rationalise the denominator,multiply the numerator and denominator by the conjugate $(4 \sqrt{3}-3 \sqrt{2})$:$= \frac{(4 \sqrt{3}+5 \sqrt{2})(4 \sqrt{3}-3 \sqrt{2})}{(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}$Divide numerator and denominator by $2$:$= \frac{9 + 4 \sqrt{6}}{15}$

Rationalise the denominator of the following:
$\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$

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Rationalise the denominator of the following:$\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$