Đáp án + giải thích các bước giải:
`((x+2)/(x\sqrt{x}-1)+(\sqrt{x}+17)/(x+\sqrt{x}+1)-1/(\sqrt{x}-1)):(\sqrt{x}-1)/2`
`=[(x+2)/((\sqrt{x}-1)(x+\sqrt{x}+1))+(\sqrt{x}+17)/(x+\sqrt{x}+1)-1/(\sqrt{x}-1)]:(\sqrt{x}-1)/2`
`=(x+2+(\sqrt{x}+17)(\sqrt{x}-1)-(x+\sqrt{x}+1))/((\sqrt{x}-1)(x+\sqrt{x}+1)) . 2/(\sqrt{x}-1)`
`=(x+2+x+17\sqrt{x}-\sqrt{x}-17-x-\sqrt{x}-1)/((\sqrt{x}-1)(x+\sqrt{x}+1)) . 2/(\sqrt{x}-1)`
`=(x+15\sqrt{x}-16)/((\sqrt{x}-1)(x+\sqrt{x}+1)) . 2/(\sqrt{x}-1)`
`=(x-\sqrt{x}+16\sqrt{x}-16)/((\sqrt{x}-1)(x+\sqrt{x}+1)) . 2/(\sqrt{x}-1)`
`=(\sqrt{x}(\sqrt{x}-1)+16(\sqrt{x}-1))/((\sqrt{x}-1)(x+\sqrt{x}+1)) . 2/(\sqrt{x}-1)`
`=((\sqrt{x}-1)(\sqrt{x}+16))/((\sqrt{x}-1)(x+\sqrt{x}+1)) . 2/(\sqrt{x}-1)`
`=(\sqrt{x}+16)/(x+\sqrt{x}+1) . 2/(\sqrt{x}-1)`
`=(2(\sqrt{x}+16))/((\sqrt{x}-1)(x+\sqrt{x}+1))`