Question

Answer 1

`a)` Với `x >= 0,x \ne 9` có:

`P=([2\sqrt{x}]/[\sqrt{x}+3]+\sqrt{x}/[\sqrt{x}-3]-[3x+3]/[x-9]):([2\sqrt{x}-2]/[\sqrt{x}-3]-1)`

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

`P=[2x-6\sqrt{x}+x+3\sqrt{x}-3x-3]/[(\sqrt{x}-3)(\sqrt{x}+3)].[\sqrt{x}-3]/[\sqrt{x}+1]`

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

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

`P=[-3]/[\sqrt{x}+3]`

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`b)` Với `x >= 0,x \ne 9` có:

`P < -1/2<=>[-3]/[\sqrt{x}+3] < -1/2`

             `<=>[-3]/[\sqrt{x}+3]+1/2 < 0`

             `<=>[-6+\sqrt{x}+3]/[2(\sqrt{x}+3)] < 0`

             `<=>[\sqrt{x}-3]/[2(\sqrt{x}+3)] < 0`

       Mà `x >= 0,x \ne 9=>2(\sqrt{x}+3) > 0`

    `=>\sqrt{x}-3 < 0<=>\sqrt{x} < 3<=>x < 9`

          Kết hợp đk

   `=>0 <= x < 9`