Question

Помогите решить 109 номер .

Answer 1

Фото прилагается. Ответы там.

Answer 2

$1)frac{sqrt{5}-sqrt{3}}{sqrt{5}+sqrt{3}}-frac{sqrt{5}+sqrt{3}}{sqrt{5}-sqrt{3}}=\\=frac{(sqrt{5}-sqrt{3})*(sqrt{5}-sqrt{3})+(sqrt{5}+sqrt{3})*(sqrt{5}+sqrt{3})}{(sqrt{5}+sqrt{3})*(sqrt{5}-sqrt{3})}=\\=frac{5-2*sqrt{5*3}+3+5+2*sqrt{5*3}+3}{(sqrt{5})^2-(sqrt{3})^2}=\\=frac{16}{5-3}=frac{16}{2}=8$

$2)frac{11+sqrt{21}}{11-sqrt{21}}+frac{11-sqrt{21}}{11+sqrt{21}}=\\=frac{(11+sqrt{21})*(11+sqrt{21})+(11-sqrt{21})*(11-sqrt{21})}{(11-sqrt{21})*(11+sqrt{21})}=\\=frac{121+2*11*sqrt{21}+21+121-2*11*sqrt{21}+21}{(11)^2-(sqrt{21})^2}=\\=frac{242+42}{121-21}=frac{284}{100}=2,84$

$[tex]3)frac{1}{11-2sqrt{30}}-frac{1}{11+2sqrt{30}}=\\=frac{1*(11+2sqrt{30})-1*(11-2sqrt{30})}{(11-2sqrt{30})*(11+2sqrt{30})}\\=frac{11+2sqrt{30}-11+2sqrt{30}}{(11)^2-(2sqrt{30})^2}=\\=frac{4sqrt{30}}{121-4*30}=frac{4sqrt{30}}{121-120}=frac{4sqrt{30}}{1}=4sqrt{30}$

$4)frac{5}{3+2sqrt{2}}+frac{5}{3-2sqrt{2}}=\\=frac{5*(3-2sqrt{2})+5*(3+2sqrt{2})}{(3+2sqrt{2})*(3-2sqrt{2})}=\\=frac{15-6sqrt{2}+15+6sqrt{2}}{(3)^2-(2sqrt{2})^2}=\\frac{30}{9-4*2}=frac{30}{9-8}=frac{30}{1}=30$