Question

Answer 1

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

Answer 2

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

Answer 3

`f, = (sqrt x xx sqrt x + sqrt x xx sqrt y)/(sqrt y xx sqrt y + sqrt x xx sqrt y)`

`= (sqrt x(sqrt x + sqrt y))/(sqrt y(sqrt x + sqrt y))`

`= sqrt x/sqrt y`

`= sqrt(x/y)`.