化(4x³-x²-3x+3)/(x^4-x³-3x - 知识问答

化(4x³-x²-3x+3)/(x^4-x³-3x²+5x-2)为部分分式

1个回答

x^4-x³-3x²+5x-2=x^3(x-1)-(3x^2-5x+2)
=x^3(x-1)-(x-1)(3x-2)
=(x-1)*(x^3-3x+2)
4x³-x²-3x+3=(3x^3-3x)+(x^3-x^2)+3
=3x(x+1)(x-1)+x^2(x-1)+3
所以(4x³-x²-3x+3)/(x^4-x³-3x²+5x-2)=(4x^2+3x)/(x^3-3x+2)+3/(x-1)*(x^3-3x+2)

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