Giúp mình với! $i)~\frac{\sqrt5-1}{\sqrt5+1}-\frac{\sqrt5+1}{\sqrt5-1}$,$k)~\frac{\sqrt{15}-\sqrt{12}}{\sqrt5-2}-\frac{6+2\sqrt6}{\sqrt3+\sqrt2}$,$m)~\frac{10+2\sqrt{10}}{\sqrt5+\sqrt2}+\frac8{1-\sqrt5}$,$o)~\frac{\sqrt{14}}{\sqrt7}-\frac5{1+\sqrt2}+\frac{\sqrt{28}-2\sqrt3}{\sqrt7-\sqrt3}$

Question

Accepted Answer

{"userId":5419770,"userName":"Nguyễn Minh Hải"}

i)

$$\frac{\sqrt{5}-1}{\sqrt{5}+1}-\frac{\sqrt{5}+1}{\sqrt{5}-1}$$

$$=\frac{\left(\sqrt{5}-1\right)^2-\left(\sqrt{5}+1\right)^2}{\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)}$$

$$=\frac{\left(5-2\sqrt{5}+1\right)-\left(5+2\sqrt{5}+1\right)}{\left(\sqrt{5}\right)^2-1^2}$$

$$=\frac{6-2\sqrt{5}-6-2\sqrt{5}}{5-1}$$

$$=\frac{-4\sqrt{5}}{4}$$

$$=-\sqrt{5}$$

k)

$$\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}-\frac{6+2\sqrt{6}}{\sqrt{3}+\sqrt{2}}$$

$$=\frac{\sqrt{3}.\left(\sqrt{5}-2\right)}{\sqrt{5}-2}-\frac{2\sqrt{3}.\left(\sqrt{3}+\sqrt{2}\right)}{\sqrt{3}+\sqrt{2}}$$

$$=\sqrt{3}-2\sqrt{3}$$

$$=-\sqrt{3}$$

m)

$$\frac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\frac{8}{1-\sqrt{5}}$$

$$=\frac{2\sqrt{5}.\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{5}+\sqrt{2}}+\frac{8.\left(1+\sqrt{5}\right)}{\left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right)}$$

$$=2\sqrt{5}+\frac{8.\left(1+\sqrt{5}\right)}{-4}$$

$$=2\sqrt{5}-2.\left(1+\sqrt{5}\right)$$

$$=2\sqrt{5}-2-2\sqrt{5}$$

$$=-2$$

o)

$$\frac{\sqrt{14}}{\sqrt{7}}-\frac{5}{1+\sqrt{2}}+\frac{\sqrt{28}-2\sqrt{3}}{\sqrt{7}-\sqrt{3}}$$

$$=\sqrt{2}-\frac{5.\left(1-\sqrt{2}\right)}{\left(1+\sqrt{2}\right)\left(1-\sqrt{2}\right)}+\frac{2\sqrt{7}-2\sqrt{3}}{\sqrt{7}-\sqrt{3}}$$

$$=\sqrt{2}-\frac{5.\left(1-\sqrt{2}\right)}{-1}+\frac{2.\left(\sqrt{7}-\sqrt{3}\right)}{\sqrt{7}-\sqrt{3}}$$

$$=\sqrt{2}-\left(-5+5\sqrt{2}\right)+2$$

$$=7-4\sqrt{2}$$.