`P=((2x^3+x^2-x)/(x^3-1)-(x^2+x)/(x^2-1)).(x^2-1)/(2x^2+x-1)+x/(2x-1)`

Đáp án+Giải thích các bước giải:

Đặt `T=(2x^3 +x^2 -x)/(x^3 1)``-(x^2 +x)/(x^2 -1)` `(đk:xne+-1;xne1/2)`

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

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

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

_______________________________________________________________________________

$P=\dfrac{\dfrac{x^3-2x}{x^2+x+1}}{2x-1}+\dfrac{x}{2x-1}$

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

$P=\dfrac{x^3-2x}{\left(2x-1\right)\left(x^2+x+1\right)}+\dfrac{x\left(x^2+x+1\right)}{\left(2x-1\right)\left(x^2+x+1\right)}$  `(đk:xne+-1;xne1/2)`

`P=(x^3 -2x+x(x^2 +x+1))/((2x-1)(x^2 +x+1))`

`P=(2x^3 +x^2 -x)/((2x-1)(x^2 +x+1))`

`P=(x^2 +x)/(x^2 +x+1)`

`P=(x(x+1))/(x^2 +x+1)`

`P=(x^2 +x)/(x^2 +x+1)`

$\text{Vậy P = }$ $\dfrac{x^2+x}{x^2+x+1}$ `(xne+-1;1/2)`