Question

Помогите решить примеры по дз хотябы один из них
1. $frac{9}{7-4sqrt{3} }$


3.$frac{b-3}{b-2sqrt{3b}+3 }$

4.$frac{132a}{sqrt{11} }$

Answer 1

$1)frac{9}{7-4sqrt{3}}=frac{9*(7+4sqrt{3})}{(7-4sqrt{3})(7+4sqrt{3})}=frac{9*(7+4sqrt{3})}{7^{2}-(4sqrt{3})^{2}}=frac{9(7+4sqrt{3})}{49-48}=9(7+4sqrt{3})$

$3)frac{b-3}{b-2sqrt{3b} +3}=frac{(sqrt{b})^{2}-(sqrt{3})^{2}}{(sqrt{b})^{2}-2sqrt{b}*sqrt{3}+(sqrt{3})^{2}} =frac{(sqrt{b}-sqrt{3})(sqrt{b}+sqrt{3})}{(sqrt{b}-sqrt{3})^{2}} =frac{sqrt{b}+sqrt{3}}{sqrt{b}-sqrt{3}} =frac{(sqrt{b}+sqrt{3})*(sqrt{b}+sqrt{3})}{(sqrt{b}-sqrt{3})*(sqrt{b}+sqrt{3})} =frac{(sqrt{b}+)sqrt{3})^{2} }{b-3}$

$4)frac{132a}{sqrt{11}}=frac{132a*sqrt{11}}{sqrt{11}*sqrt{11}}=frac{132a*sqrt{11}}{(sqrt{11})^{2}}=frac{132a*sqrt{11}}{11}=12sqrt{11}a$