\(P=\left(\dfrac{1}{x-1}-\dfrac{2x}{x^3-x^2+x-1}\right):\left(\dfrac{1-2x}{x+1}\right)\left(ĐKXĐ:x\ne0;x\ne\pm1\right)\)

\(=\left(\dfrac{1}{x-1}-\dfrac{2x}{x^2\left(x-1\right)+\left(x-1\right)}\right):\left(\dfrac{1-2x}{x+1}\right)\)

\(=\left(\dfrac{1}{x-1}-\dfrac{2x}{\left(x-1\right)\left(x^2+1\right)}\right):\left(\dfrac{1-2x}{x+1}\right)\)

\(=\left(\dfrac{x^2+1-2x}{\left(x-1\right)\left(x^2+1\right)}\right):\left(\dfrac{1-2x}{x+1}\right)\)

\(=\dfrac{\left(x-1\right)^2}{\left(x-1\right)\left(x^2+1\right)}:\dfrac{1-2x}{x+1}\)

\(=\dfrac{x-1}{x^2+1}:\dfrac{1-2x}{x+1}\)

\(=\dfrac{x-1}{x^2+1}.\dfrac{x+1}{1-2x}\)

\(=\dfrac{x^2-1}{\left(x^2+1\right)\left(1-2x\right)}\)

Ta có: P = x − x + 2 ( x + 1 ) ( x − 2 ) − x x ( x − 2 ) : 1 − x 2 − x = x − x + 2 − x ( x + 1 ) ( x + 1 ) ( x − 2 ) . 2 − x 1 − x = 2 − 2 x ( x + 1 ) ( x − 1 ) = 2 ( 1 − x ) ( x + 1 ) ( x − 1 ) = − 2 x + 1  

cho biểu thức A 2√x xx√x−1 −1√x−1 √x 2x √x 1 a rút gọn biểu thứcb tính giá trị của √Akhi x 4 2√3.

a) Ta có: \(\left(x+1\right)\left(x^2-x+1\right)-\left(x-1\right)\left(x^2+x+1\right)\)

\(=x^3+1-x^3+1\)

=2

b) Ta có: \(\left(2x+3\right)\left(2x-3\right)-\left(2x+1\right)^2\)

\(=4x^2-9-4x^2-4x-1\)

\(=-4x-10\)

\(\left(\dfrac{\dfrac{x}{x+1}}{\dfrac{x^2}{x^2+x+1}}-\dfrac{2x+1}{x^2+x}\right)\dfrac{x^2-1}{x-1}\)ĐK : \(x\ne\pm1\)

\(=\left(\dfrac{x}{x+1}.\dfrac{x^2+x+1}{x^2}-\dfrac{2x+1}{x\left(x+1\right)}\right)\left(x+1\right)=\left(\dfrac{x^2+x-1}{x^2+x}-\dfrac{2x+1}{x\left(x+1\right)}\right)\left(x+1\right)\)

\(=\left(\dfrac{x^2+x-1-2x-1}{x\left(x+1\right)}\right)\left(x+1\right)=\dfrac{x^2-3x-2}{x}\)

à xin lỗi mình nhầm dòng cuối 

\(=\dfrac{x^2-x-2}{x}=\dfrac{\left(x+1\right)\left(x-2\right)}{x}\)

Để biểu thức trên nhận giá trị dương khi 

\(\dfrac{\left(x+1\right)\left(x-2\right)}{x}>0\)bạn tự xét TH cả tử và mẫu nhé, mình đánh trên này bị lỗi