Question

P= (1/x-1 - 2x/ x^3 - x^2 +x -1) : ( 1-2x/x+1) (x khác 0, x khác +1 hoặc -1
a) rút gọn P
 

Answer 1

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

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

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

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

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

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

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

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