$\frac{5-3√5}{√5-3}$- $\frac{8}{√5-1}$+ $\frac{1- √5}{ √5}$

Đáp án:

`(5-3\sqrt{5})/(\sqrt{5}-3)-8/(\sqrt{5}-1)+(1-\sqrt{5})/\sqrt{5}`

`=(-4\sqrt5-15)/5`

Giải thích các bước giải:

`(5-3\sqrt{5})/(\sqrt{5}-3)-8/(\sqrt{5}-1)+(1-\sqrt{5})/\sqrt{5}`

`=((5-3\sqrt{5})(\sqrt{5}+3))/((\sqrt{5}-3)(\sqrt{5}+3))-(8(\sqrt{5}+1))/((\sqrt{5}-1)(\sqrt{5}+1))+((1-\sqrt{5})\sqrt{5})/(\sqrt{5}\sqrt{5})`

`=((5-3\sqrt{5})(\sqrt{5}+3))/((\sqrt{5})^2-3^2)-(8(\sqrt{5}+1))/((\sqrt{5})^2-1)+((1-\sqrt{5})\sqrt{5})/5`

`=((5-3\sqrt{5})(\sqrt{5}+3))/(5-9)-(8(\sqrt{5}+1))/(5-1)+((1-\sqrt{5})\sqrt{5})/5`

`=-[(5-3\sqrt{5})(\sqrt{5}+3)]/4-(8(\sqrt{5}+1))/4+(\sqrt{5}-5)/5`

`=(-5\sqrt{5}-15+15+9\sqrt{5})/4-(8(\sqrt{5}+1))/4+(\sqrt{5}-5)/5`

`=(4\sqrt{5})/4-(8(\sqrt{5}+1))/4+(\sqrt{5}-5)/5`

`=\sqrt{5}-2\sqrt{5}-2+(\sqrt{5}-5)/5`

`=-\sqrt{5}-2+(\sqrt{5}-5)/5`

`=(-5\sqrt{5})/5-10/5+(\sqrt{5}-5)/5`

`=(-5\sqrt{5}-10+\sqrt{5}-5)/5`

`=(-4\sqrt5-15)/5`