Question

Cho P= \(\dfrac{1}{\sqrt{x}+2}+\dfrac{x+8}{x-4}-\dfrac{3}{\sqrt{x}-2}\) (x≥0; x≠4)

a) Rút gọn P

b)Tìm x sao cho P<\(\dfrac{1}{5}\)

Answer 1

`a)` Với `x >= 0,x \ne 4` có:

`P=[\sqrt{x}-2+x+8-3(\sqrt{x}+2)]/[(\sqrt{x}-2)(\sqrt{x}+2)]`

`P=[\sqrt{x}-2+x+8-3\sqrt{x}-6]/[(\sqrt{x}-2)(\sqrt{x}+2)]`

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

`P=\sqrt{x}/[\sqrt{x}+2]`

___________________________________________

`b)` Với `x >= 0,x \ne 4` có:

`P < 1/5<=>\sqrt{x}/[\sqrt{x}+2]-1/5 < 0`

      `<=>[5\sqrt{x}-\sqrt{x}-2]/[5(\sqrt{x}+2)] < 0`

         Mà `5(\sqrt{x}+2) > 0`

  `=>4\sqrt{x}-2 < 0`

`<=>\sqrt{x} < 1/2`

`<=>x < 1/2`

Kết hợp đk

  `=>0 <= x < 1/2`