Question

rút gọn

\(\dfrac{1}{\sqrt{7}-\sqrt{3}}-\dfrac{1}{\sqrt{7}+\sqrt{3}}\)

Answer 1

ta có \(\dfrac{1}{\sqrt{7}-\sqrt{3}}-\dfrac{1}{\sqrt{7}+\sqrt{3}}\)

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

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

=\(\dfrac{2\sqrt{3}}{7-3}=\dfrac{2\sqrt{3}}{2}\)=\(\sqrt{3}\)

Answer 2

-đẻ rút gọn ta đi quy đồng mẫu các hạng tử:

\(\dfrac{1}{\sqrt{7}-\sqrt{3}}-\dfrac{1}{\sqrt{7}+\sqrt{3}}\Rightarrow\dfrac{\left(\sqrt{7}+\sqrt{3}\right)}{\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)}-\dfrac{\left(\sqrt{7}-\sqrt{3}\right)}{\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)}\Rightarrow\dfrac{2\sqrt{3}}{\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)}=\dfrac{2\sqrt{3}}{4}=\dfrac{\sqrt{3}}{2}\)