Question

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


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

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

Answer 1

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

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

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