Toán Rút gọn phân thức: `A={2x^3+x^2-2x-1}/{x^3+2x^2-x-2}` 23/11/2021 By Alexandra Rút gọn phân thức: `A={2x^3+x^2-2x-1}/{x^3+2x^2-x-2}`
`\text{~~Holi~~}` `A=(2x^3+x^2-2x-1)/(x^3+2x^2-x-2)` `= (x^2(2x+1)-(2x+1))/(x^2(x+2)-(x+2))` `= ((2x+1)(x^2-1))/((x+2)(x^2-1))` `= (2x+1)/(x+2)` Trả lời
`~rai~` $\begin{array}{I}A=\dfrac{2x^3+x^2-2x-1}{x^3+2x^2-x-2}\\A=\dfrac{(2x^3-2x)+(x^2-1)}{(x^3-x)+(2x^2-2)}\\A=\dfrac{2x(x^2-1)+(x^2-1)}{x(x^2-1)+2(x^2-1)}\\A=\dfrac{(2x+1)(x^2-1)}{(x+2)(x^2-1)}\\A=\dfrac{2x+1}{x+2}.\end{array}$ Trả lời
`\text{~~Holi~~}`
`A=(2x^3+x^2-2x-1)/(x^3+2x^2-x-2)`
`= (x^2(2x+1)-(2x+1))/(x^2(x+2)-(x+2))`
`= ((2x+1)(x^2-1))/((x+2)(x^2-1))`
`= (2x+1)/(x+2)`
`~rai~`
$\begin{array}{I}A=\dfrac{2x^3+x^2-2x-1}{x^3+2x^2-x-2}\\A=\dfrac{(2x^3-2x)+(x^2-1)}{(x^3-x)+(2x^2-2)}\\A=\dfrac{2x(x^2-1)+(x^2-1)}{x(x^2-1)+2(x^2-1)}\\A=\dfrac{(2x+1)(x^2-1)}{(x+2)(x^2-1)}\\A=\dfrac{2x+1}{x+2}.\end{array}$