Question

Rút gọn

A=\(\dfrac{1}{2+\sqrt{x}}+\dfrac{1}{2-\sqrt{x}}-\dfrac{2\sqrt{x}}{4-x}\)

B=\(\left(\sqrt{2}+\sqrt{3}\right):\sqrt{2}-\sqrt{6}+\dfrac{\sqrt{333}}{\sqrt{111}}\)

Answer 1

\(A=\dfrac{1}{2+\sqrt{x}}+\dfrac{1}{2-\sqrt{x}}-\dfrac{2\sqrt{x}}{4-\sqrt{x}}\)

\(A=\dfrac{1}{2+\sqrt{x}}+\dfrac{1}{2-\sqrt{x}}-\dfrac{2\sqrt{x}}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}\)

\(A=\dfrac{2-\sqrt{x}+2+\sqrt{x}-2\sqrt{x}}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}\)

\(A=\dfrac{4-2\sqrt{x}}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}=\dfrac{2\left(2-\sqrt{x}\right)}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}=\dfrac{2}{2+\sqrt{x}}\)

Answer 2

\(B=\left(\sqrt{2}+\sqrt{3}\right)+\sqrt{2}-\sqrt{6}+\dfrac{\sqrt{333}}{\sqrt{111}}\)

\(=\dfrac{\sqrt{2}+\sqrt{3}}{\sqrt{2}}-\sqrt{6}+\sqrt{3}\)

\(=\dfrac{\left(\sqrt{2}+\sqrt{3}\right)\sqrt{2}}{2}-\sqrt{6}+\sqrt{3}\)

\(=\dfrac{2+\sqrt{6}}{2}-\sqrt{6}+\sqrt{3}\)

\(=\dfrac{2+\sqrt{6}-2\sqrt{6}}{2}+\sqrt{3}\)

\(=\dfrac{2-\sqrt{6}}{2}+\sqrt{3}\)