Question

Cho biểu thức P= \(\dfrac{x+2\sqrt{x}-11}{x+4\sqrt{x}+3}+\dfrac{\sqrt{x}-1}{\sqrt{x}+3}-\dfrac{\sqrt{x}-3}{\sqrt{x}+1}\)

1. Rút gọn

2.Tính P khi x=3-\(2\sqrt{2}\)

Answer 1

`P=(x+2\sqrtx-11)/(x+4sqrtx+3)+(sqrtx-1)/(sqrtx+3)-(sqrtx-3)/(sqrtx+1)`

`đkxđ:x>=0`

`P=(x+2sqrtx-11+(sqrtx-1)(sqrtx+1)-(sqrtx-3)(sqrtx+3))/(x+4sqrtx+3)`

`=(x+2sqrtx-11+x-1-x+9)/(x+4sqrtx+3)`

`=(x+2sqrtx-3)/(x+4sqrtx+3)`

`=((sqrtx+1)(sqrtx-3))/((sqrtx+1)(sqrtx+3))`

`=(sqrtx-3)/(sqrtx+3)`

`2)x=3-2sqrt2=(sqrt2-1)^2`

`=>P=(sqrt2-1-3)/(sqrt2-1+3)`

`=(sqrt2-4)/(sqrt2+2)`

`=-(4-sqrt2)(2-sqrt2)`

`=-(8-6sqrt2+2)`

`=-10+6sqrt2`