+15001 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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