a: Ta có: \(\dfrac{x^3-3x+2}{\left(x-1\right)^2}\)
\(=\dfrac{x^3-x-2x+2}{\left(x-1\right)^2}\)
\(=\dfrac{x\left(x-1\right)\left(x+1\right)-2\left(x-1\right)}{\left(x-1\right)^2}\)
\(=\dfrac{\left(x-1\right)\left(x^2+x-2\right)}{\left(x-1\right)^2}\)
\(=x+2\)
b: Ta có: \(\dfrac{3x^4-4x^3+1}{\left(x-1\right)^2}\)
\(=\dfrac{3x^4-3x^3-x^3+1}{\left(x-1\right)^2}\)
\(=\dfrac{3x^3\left(x-1\right)-\left(x-1\right)\left(x^2+x+1\right)}{\left(x-1\right)^2}\)
\(=\dfrac{3x^3-x^2-x-1}{x-1}\)
\(=\dfrac{3x^3-3x^2+2x^2-2x+x-1}{x-1}\)
\(=3x^2+2x+1\)
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