Question

Thực hiện phép tính:

\(\frac{1}{5-\sqrt{3}}-\frac{1}{5+\sqrt{3}}\)

Answer 1

\(\frac{5+\sqrt{3}-5+\sqrt{3}}{25-3}=\frac{2\sqrt{3}}{22}=\frac{\sqrt{3}}{11}\\ \)

học tốt 

Answer 2

\(\frac{1}{5-\sqrt{3}}-\frac{1}{5+\sqrt{3}}\)

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

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

\(=\frac{5+\sqrt{3}-\left(5-\sqrt{3}\right)}{22}\)

\(=\frac{5+\sqrt{3}-5+\sqrt{3}}{22}\)

\(=\frac{2\sqrt{3}}{22}=\frac{\sqrt{3}}{11}\)