Toán ((2x+1)/(x√x-1)-√x/(x+√x+1)).((1+x√x)/(1+√x)-√x) rút gọn biểu thức 17/07/2021 By Savannah ((2x+1)/(x√x-1)-√x/(x+√x+1)).((1+x√x)/(1+√x)-√x) rút gọn biểu thức
Đáp án+Giải thích các bước giải: Với `x≥0;x\ne1` `((2x+1)/(x\sqrtx-1)-\sqrtx/(x+\sqrtx+1)).((1+x\sqrtx)/(1+\sqrtx)-\sqrtx)` `=((2x+1)/((\sqrtx-1)(x+\sqrtx+1))-\sqrtx/(x+\sqrtx+1)).(((\sqrtx+1)(x-\sqrtx+1))/(1+\sqrtx)-\sqrtx)` `=(2x+1-\sqrtx(\sqrtx-1))/((\sqrtx-1)(x+\sqrtx+1)).(x-\sqrtx+1-\sqrtx)` `=(2x+1-x+\sqrtx)/((\sqrtx-1)(x+\sqrtx+1)).(x-2\sqrtx+1)` `=(x+\sqrtx+1)/((\sqrtx-1)(x+\sqrtx+1)).(\sqrtx-1)^2` `=1/(\sqrtx-1).(\sqrtx-1)^2` `=(\sqrtx-1)^2/(\sqrtx-1)` `=\sqrtx-1` Trả lời
Đáp án+Giải thích các bước giải:
Với `x≥0;x\ne1`
`((2x+1)/(x\sqrtx-1)-\sqrtx/(x+\sqrtx+1)).((1+x\sqrtx)/(1+\sqrtx)-\sqrtx)`
`=((2x+1)/((\sqrtx-1)(x+\sqrtx+1))-\sqrtx/(x+\sqrtx+1)).(((\sqrtx+1)(x-\sqrtx+1))/(1+\sqrtx)-\sqrtx)`
`=(2x+1-\sqrtx(\sqrtx-1))/((\sqrtx-1)(x+\sqrtx+1)).(x-\sqrtx+1-\sqrtx)`
`=(2x+1-x+\sqrtx)/((\sqrtx-1)(x+\sqrtx+1)).(x-2\sqrtx+1)`
`=(x+\sqrtx+1)/((\sqrtx-1)(x+\sqrtx+1)).(\sqrtx-1)^2`
`=1/(\sqrtx-1).(\sqrtx-1)^2`
`=(\sqrtx-1)^2/(\sqrtx-1)`
`=\sqrtx-1`