Question

Rút gọn biểu thức

\(\dfrac{\left(\sqrt{3}-\sqrt{5}\right)^2+4\sqrt{15}}{\sqrt{3}+\sqrt{5}}\)

Answer 1

\(\dfrac{\left(\sqrt{3}-\sqrt{5}\right)^2+4\sqrt{15}}{\sqrt{3}+\sqrt{5}}\)

= \(\dfrac{\sqrt{3}^2-2\sqrt{15}+\sqrt{5}^2+4\sqrt{15}}{\sqrt{3}+\sqrt{5}}\)

= \(\dfrac{8+2\sqrt{15}}{\sqrt{3}+\sqrt{5}}\)

=\(\dfrac{\sqrt{3}^2+2.\sqrt{3}.\sqrt{5}+\sqrt{15}^{15}}{\sqrt{3}+\sqrt{5}}\)

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

=\(\sqrt{5}+\sqrt{3}\)

Answer 2

Mình sửa chút nha: \(\dfrac{\sqrt{3}^2+2.\sqrt{3}.\sqrt{5}+\sqrt{5}^2}{\sqrt{3}+\sqrt{5}}\)