1/căn 5 + căn 3 -1/ căn 5 - căn 3

Đáp án+Giải thích các bước giải:

`\frac{1}{\sqrt{5}+\sqrt{3}}-\frac{1}{\sqrt{5}-\sqrt{3}}`

`=\frac{\sqrt{5}-\sqrt{3}}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}-\frac{\sqrt{5}+\sqrt{3}}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}`

`=\frac{\sqrt{5}-\sqrt{3}}{5-3}-\frac{\sqrt{5}+\sqrt{3}}{5-3}`

`=\frac{\sqrt{5}-\sqrt{3}}{2}-\frac{\sqrt{5}+\sqrt{3}}{2}`

`=\frac{\sqrt{5}-\sqrt{3}-\sqrt{5}-\sqrt{3}}{2}`

`=\frac{-2\sqrt{3}}{2}`

`=-\sqrt{3}`

Đáp án:

$-\sqrt{3}$

Giải thích các bước giải:

$\dfrac{1}{\sqrt{5}+\sqrt{3}}-\dfrac{1}{\sqrt{5}-\sqrt{3}}$

$=\dfrac{\sqrt{5}-\sqrt{3}}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}-\dfrac{\sqrt{5}+\sqrt{3}}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}$

$=\dfrac{\sqrt{5}-\sqrt{3}-\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}$

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

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

$=-\sqrt{3}$