Question

Answer 1

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

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

\(\Rightarrow\dfrac{x^2-x+2}{\left(x-1\right)^3}=\dfrac{C.x^2-\left(2C-B\right)x+A-B+C}{\left(x-1\right)^3}\)

Đồng nhất hệ số tử số 2 vế:

\(\Rightarrow\left\{{}\begin{matrix}C=1\\2C-B=1\\A-B+C=2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}C=1\\B=1\\A=2\end{matrix}\right.\)