rút gọn các biểu thức sau

Đáp án+Giải thích các bước giải:

17)
`P_(17)=(x^2-\sqrtx)/(x+\sqrtx+1)-(2x+\sqrtx)/\sqrtx+(2(x-1))/(\sqrtx-1)`
ĐKXĐ: `x>0;xne1`
`=(\sqrtx(x\sqrtx-1))/(x+\sqrtx+1)-(\sqrtx(2\sqrtx+1))/\sqrtx+(2(\sqrtx-1)(\sqrtx+1))/(\sqrtx-1)`

`=(\sqrtx(\sqrtx-1)(x+\sqrtx+1))/(x+\sqrtx+1)-(\sqrtx(2\sqrtx+1))/\sqrtx+(2(\sqrtx-1)(\sqrtx+1))/(\sqrtx-1)`

`=\sqrtx(\sqrtx-1)-(2\sqrtx+1)+2(\sqrtx+1)`

`=x-\sqrtx`

Vậy `P_(17)=x-\sqrtx`

18)

`P_(18)=(x\sqrtx+26\sqrtx-19)/(x+2\sqrtx-3)-(2\sqrtx)/(\sqrtx-1)+(\sqrtx-3)/(\sqrtx+3)`
ĐKXĐ:`x>=0;xne1`
`=(x\sqrtx+26\sqrtx-19)/(x-\sqrtx+3\sqrtx-3)-(2\sqrtx)/(\sqrtx-1)+(\sqrtx-3)/(\sqrtx+3)`

`=(x\sqrtx+26\sqrtx-19)/(\sqrtx(\sqrtx-1)+3(\sqrtx-1))-(2\sqrtx)/(\sqrtx-1)+(\sqrtx-3)/(\sqrtx+3)`
`=(x\sqrtx+26\sqrtx-19)/((\sqrtx+3)(\sqrtx-1))-(2\sqrtx)/(\sqrtx-1)+(\sqrtx-3)/(\sqrtx+3)`

`=(x\sqrtx+26\sqrtx-19-2\sqrtx (\sqrtx+3)+(\sqrtx-3)(\sqrtx-1))/((\sqrtx+3)(\sqrtx-1))`

`=(x\sqrtx+26\sqrtx-19-2x-6\sqrtx+x-\sqrtx-3\sqrtx+3)/((\sqrtx+3)(\sqrtx-1))`
`=(x\sqrtx -x+16\sqrtx-16)/((\sqrtx+3)(\sqrtx-1))`
`=(x(\sqrtx-1)+16(\sqrtx-1))/((\sqrtx+3)(\sqrtx-1))`
`=((x+16)(\sqrtx-1))/((\sqrtx+3)(\sqrtx-1))`
`=(x+16)/(\sqrtx+3)`

`=((x+16)(\sqrtx-3))/((\sqrtx)^2-3^2)`
`=(x\sqrtx-3\sqrtx+16\sqrtx-48)/(x-9)`

Vậy `P_(18)=(x\sqrtx-3\sqrtx+16\sqrtx-48)/(x-9)`