`a,`

ĐKXĐ: `x > 0;\ x \ne 1;\ x \ne 4`

`P = [ \frac{\sqrt{x}}{3 + \sqrt{x}} + \frac{x + 9}{9 - x} ] : [ \frac{3\sqrt{x} + 1}{x - 3\sqrt{x}} - \frac{1}{\sqrt{x}} ]`

`P= [ \frac{\sqrt{x}(3 - \sqrt{x}) + (x + 9)}{(3 + \sqrt{x})(3 - \sqrt{x})} ] : [ \frac{3\sqrt{x} + 1 - (\sqrt{x} - 3)}{\sqrt{x}(\sqrt{x} - 3)} ]`

`P= [ \frac{3\sqrt{x} - x + x + 9}{9 - x}] : [ \frac{2\sqrt{x} + 4}{\sqrt{x}(\sqrt{x} - 3)} ]`

`P= [ \frac{3\sqrt{x} + 9}{9 - x} ] : [ \frac{2\sqrt{x} + 4}{\sqrt{x}(\sqrt{x} - 3)} ]`

`P= [\frac{3(\sqrt{x} + 3)}{(3 + \sqrt{x})(3 - \sqrt{x})} ] :[ \frac{2(\sqrt{x} + 2)}{\sqrt{x}(\sqrt{x} - 3)} ]`

`P= \frac{3(\sqrt{x} + 3)\sqrt{x}(\sqrt{x} - 3)}{(3 + \sqrt{x})(3 - \sqrt{x}) \cdot 2(\sqrt{x} + 2)}`

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

`P= \frac{3\sqrt{x} \cdot (-1)(3 - \sqrt{x})}{2(\sqrt{x} + 2)(3 - \sqrt{x})}`

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

`b,`

Để `P<-1`

`\frac{-3\sqrt{x}}{2(\sqrt{x} + 2)} < -1 `

`\Rightarrow \frac{-3\sqrt{x}}{2(\sqrt{x} + 2)} + 1 < 0`

`\Rightarrow \frac{-3\sqrt{x} + 2(\sqrt{x} + 2)}{2(\sqrt{x} + 2)} < 0 `

`\Rightarrow \frac{-3\sqrt{x} + 2\sqrt{x} + 4}{2(\sqrt{x} + 2)} < 0 `

`\Rightarrow \frac{-\sqrt{x} + 4}{2(\sqrt{x} + 2)} < 0 `

`\Rightarrow \frac{4 - \sqrt{x}}{2(\sqrt{x} + 2)} < 0`

Ta có:

`2(\sqrt{x} + 2) > 0` với mọi `x > 0`

`=> 4 - \sqrt{x} < 0`

`\Rightarrow \sqrt{x} > 4`

`\Rightarrow x > 16` 

Vậy `...`