Question

Answer 1

`a)` Với `x >= 0,x \ne 1`. Ta có:

`H=\sqrt{x}/[\sqrt{x}+1]+3/[\sqrt{x}-1]-2/[x-1]`

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

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

`H=[x+2\sqrt{x}+1]/[(\sqrt{x}-1)(\sqrt{x}+1)]`

`H=[(\sqrt{x}+1)^2]/[(\sqrt{x}-1)(\sqrt{x}+1)]`

`H=[\sqrt{x}+1]/[\sqrt{x}-1]`

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`b)` Với `x=4` t/m đk

Thay `x=4` vào `H` có:

`H=[\sqrt{4}+1]/[\sqrt{4}-1]=3`