`(xsqrt{x} + 2x)/(sqrt{x} + 2) + (9-x)/(3 + sqrt{x}) - x `
`= (x(sqrt{x} + 2))/(sqrt{x} + 2) + ((3-sqrt{x})(3+sqrt{x}))/(3 + sqrt{x}) - x`
`= x + 3-sqrt{x} - x `
`= 3-sqrt{x}`
`((2 - xsqrt{x})/(2-sqrt{x}) + sqrt{x}) : (2-x)/(2-sqrt{x})`
`=(2 - xsqrt{x})/(2-sqrt{x}) : (2-x)/(2-sqrt{x}) + sqrt{x} : (2-x)/(2-sqrt{x}) `
`= (2 - xsqrt{x})/(2-sqrt{x}) . (2-sqrt{x})/(2-x) + sqrt{x} . (2-sqrt{x})/(2-x)`
`= (2 - xsqrt{x})/(2-x) + ((2-sqrt{x})sqrt{x})/(2-x)`
`= (2 - xsqrt{x})/(2-x) + (2sqrt{x} -x)/(2-x)`
`= (2 - xsqrt{x} + 2sqrt{x} -x)/(2-x)`
`= ((2-x) + (2sqrt{x} - xsqrt{x} ))/(2-x)`
`= ((2-x) + sqrt{x} (2 - x))/(2-x)`
`= 1 + sqrt{x} `
\(\dfrac{x\sqrt{x}+2x}{\sqrt{x}+2}+\dfrac{9-\sqrt{x}}{3+\sqrt{x}}-x\)
\(=\dfrac{x\left(\sqrt{x}+2\right)}{\sqrt{x}+2}+\dfrac{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}{3+\sqrt{x}}-x\)
\(=x-x+3-\sqrt{x}=3-\sqrt{x}\)
\(\left(\dfrac{2-x\sqrt{x}}{2-\sqrt{x}}+\sqrt{x}\right):\dfrac{2-x}{2-\sqrt{x}}\)
\(=\dfrac{2-x\sqrt{x}+2\sqrt{x}-x}{2-\sqrt{x}}\cdot\dfrac{2-\sqrt{x}}{2-x}\)
\(=\dfrac{\left(2-x\right)+\sqrt{x}\left(2-x\right)}{2-x}=\dfrac{\left(2-x\right)\left(1+\sqrt{x}\right)}{2-x}=1+\sqrt{x}\)
