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$\frac{1}{5+2 \sqrt{6} } + \frac{1}{5-2 \sqrt{6} } = \frac{5-2 \sqrt{6} +5+2 \sqrt{6} }{25-24} = 10$

$[18 \frac{1}{6} -(3,06:7 \frac{1}{2}+3 \frac{2}{5} *0,38)]:(19-2 \frac{3}{8} *5 \frac{1}{3} )=2,6$
1) 3,06:7,5=0,408
2) 3,4*0,38=1,922
3) 0,408+1,922=1,7
4) 18 $\frac{1}{6} -1 \frac{7}{10} =17 \frac{35}{30} -1 \frac{21}{30} =16 \frac{14}{30} =16 \frac{7}{15}$
5) $2 \frac{3}{8} *5 \frac{1}{3} = \frac{19}{8} * \frac{16}{3} = \frac{38}{3} =12 \frac{2}{3}$
6) 1= $19-12 \frac{2}{3} =6 \frac{1}{3}$
7) $16 \frac{7}{15}:6 \frac{1}{3} = \frac{247}{95} =2,6$