a)Với `x >= 0; x!= 1`

`A = (\sqrt{x})/(\sqrt{x}-1) + 1/(\sqrt{x}+2) + (3\sqrt{x})/(-x-\sqrt{x}+2)`

`A = (\sqrt{x}(\sqrt{x}+2) + (\sqrt{x}-1) - 3\sqrt{x}) / ((\sqrt{x}-1)(\sqrt{x}+2))`

`A = (x + 2\sqrt{x} + \sqrt{x} - 1 - 3\sqrt{x}) / ((\sqrt{x}-1)(\sqrt{x}+2))`

`A = (x - 1) / ((\sqrt{x}-1)(\sqrt{x}+2))`

`A = ((\sqrt{x}-1)(\sqrt{x}+1)) / ((\sqrt{x}-1)(\sqrt{x}+2))`

`A = (\sqrt{x}+1) / (\sqrt{x}+2)`

b)`S = ((\sqrt{x}+1) / (\sqrt{x}+2)) * ((\sqrt{x}+3) / (\sqrt{x}+1))`

`S = (\sqrt{x}+3) / (\sqrt{x}+2)`

`S - (3)/(2) = (\sqrt{x}+3) / (\sqrt{x}+2) - (3)/(2)`

`= (2(\sqrt{x}+3) - 3(\sqrt{x}+2)) / (2(\sqrt{x}+2))`

`= (2\sqrt{x} + 6 - 3\sqrt{x} - 6) / (2(\sqrt{x}+2))`

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

`-\sqrt{x} <= 0; 2(\sqrt{x}+2) > 0` `(x>=0; x!= 1)`

`->(-\sqrt{x}) / (2(\sqrt{x}+2)) <= 0 `

`=> S - (3)/(2) <= 0 => S <= (3)/(2)`