Question

bài 1 :rút gọn

\(\dfrac{x+y-2\sqrt{xy}}{\sqrt{x}-\sqrt{y}}-\dfrac{x+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\)

bài 2 ; tính

\(\sqrt{\left(1-2\right)^2}+\dfrac{3}{\sqrt{2}}-\sqrt{\dfrac{1}{2}}\)

Answer 1

bài 1

\(\dfrac{x+y-2\sqrt{xy}}{\sqrt{x}-\sqrt{y}}-\dfrac{x+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\)

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

=\(\sqrt{x}-\sqrt{y}-\sqrt{x}=-\sqrt{y}\)

Answer 2

bài 2

\(\sqrt{\left(1-2\right)^2}+\dfrac{3}{\sqrt{2}}-\sqrt{\dfrac{1}{2}}\)

=\(\left|1-2\right|+\dfrac{3}{\sqrt{2}}-\dfrac{\sqrt{1}}{\sqrt{2}}\)

= 1+\(\dfrac{3-1}{\sqrt{2}}=1+\dfrac{2}{\sqrt{2}}=1+\sqrt{2}\)