Question

[Lâm Phương Thảo]

Rút gọn các biểu thức :

a) Rút gọn biểu thức : \(\frac{1}{3-\sqrt{7}}-\frac{1}{3+\sqrt{7}}\)

Answer 1

[l҉o҉n҉g҉ d҉z҉]

\(\frac{1}{3-\sqrt{7}}-\frac{1}{3+\sqrt{7}}=\frac{3+\sqrt{7}}{\left(3-\sqrt{7}\right)\left(3+\sqrt{7}\right)}-\frac{3-\sqrt{7}}{\left(3-\sqrt{7}\right)\left(3+\sqrt{7}\right)}\)

\(=\frac{3+\sqrt{7}-3+\sqrt{7}}{\left(3-\sqrt{7}\right)\left(3+\sqrt{7}\right)}=\frac{2\sqrt{7}}{9-7}=\sqrt{7}\)

Answer 2

[Nguyễn Huy Tú]

a, \(\frac{1}{3-\sqrt{7}}-\frac{1}{3+\sqrt{7}}=\frac{3+\sqrt[]{7}-3+\sqrt{7}}{\left(3-\sqrt{7}\right)\left(3+\sqrt{7}\right)}\)

\(=\frac{2\sqrt{7}}{9-7}=\sqrt{7}\)