Question

\(\dfrac{\left(\sqrt{x}+\sqrt{y}\right)^2-4\sqrt{xy}}{\sqrt{x}-\sqrt{y}}\) + \(\dfrac{x\sqrt{y}-y\sqrt{x}}{\sqrt{xy}}\)

\(\dfrac{x-1}{\sqrt{y}-1}\) . \(\sqrt{\dfrac{\left(y-2\sqrt{y}+1\right)^2}{\left(x-1\right)^4}}\)

 

Answer 1

`((sqrt{x} + sqrt{y})^2 - 4sqrt{xy})/(sqrt{x} - sqrt{y} + (x sqrt{y} - y sqrt{x})/sqrt{xy} `

`ĐKXĐ: x;y >0; x ne y`

`Bt = (sqrt{x}^2 + 2 sqrt{x}sqrt{y} + sqrt{y}^2 - 4sqrt{xy})/(sqrt{x} - sqrt{y}) + sqrt{x} - sqrt{y}`

`= (sqrt{x}^2 + 2 sqrt{xy} + sqrt{y}^2 - 4sqrt{xy})/(sqrt{x} - sqrt{y}) + sqrt{x} - sqrt{y}`

`= (sqrt{x}^2 - 2 sqrt{xy} + sqrt{y}^2)/(sqrt{x} - sqrt{y}) + sqrt{x} - sqrt{y}`

`= ((sqrt{x} - sqrt{y})^2)/(sqrt{x} - sqrt{y}) + sqrt{x} - sqrt{y}`

`= sqrt{x} - sqrt{y} + sqrt{x} - sqrt{y}`

`= 2sqrt{x} + 2 sqrt{y}`

Answer 2