Răspuns:
[tex]\large\bf\purple{\underline{3 \sqrt{2} - 3 \sqrt{3} }}[/tex]
Explicație pas cu pas:
[tex]\bf{ \frac{1}{5 \sqrt{2} + 4 \sqrt{3} } - \frac{1}{3 \sqrt{2} + 2 \sqrt{3} } - \frac{10}{4 \sqrt{3} + 3 \sqrt{2} } = \frac{3(5 \sqrt{2} - 4 \sqrt{3} ) - (3 \sqrt{2} - 2 \sqrt{3}) - 2(4 \sqrt{3} - 3 \sqrt{2} )}{6} = }[/tex]
[tex]\bf{ \frac{15 \sqrt{2} - 12 \sqrt{3} - 3 \sqrt{2} + 2 \sqrt{3} - 8 \sqrt{3} + 6 \sqrt{2} }{6} = \frac{18 \sqrt{2} - 18 \sqrt{3} }{6} = \frac{6(3 \sqrt{2} - 3 \sqrt{3}) }{6} =\large\bf\purple{\underline{3 \sqrt{2} - 3 \sqrt{3} }} }[/tex]
