please help

Rationalize the denominator

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$\frac{5\sqrt{3}-4 \sqrt{2}}{4\sqrt{3}+3\sqrt{2}}$

$\sqrt{2}=a,\ \sqrt{3}=b$

$=\frac{5b-4a}{4b+3a}{\color{blue}\times\frac{4b-3a}{4b-3a}}=\frac{20b^2-15ab-16ab+12a^2}{16b^2-9a^2}$

$=\frac{20b^2-31ab+12a^2}{16b^2-9a^2}$

$a=\sqrt{2},\ b=\sqrt{3}$

$=\frac{20\cdot 3-31\sqrt{2\cdot 3}+12\cdot 2}{16\cdot 3-9\cdot 2}$

$=\frac{84-31\sqrt{6}}{30}=0.26886$

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