将](X^2+1)/(X+1)^2(X+2)化为部分分式 将分式(2x^2+x+2)/(x^3+1)化为部分分式
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1.(x^2+1)/(x+1)^2(x+2)
=(x^2-2x-3+2x+4)/(x^2+1)^2(x+2)
=(x+1)(x-3)/(x+1)^2(x+2)+2(x+2)/(x+1)^2(x+2)
=(x-3)/(x+1)(x+2)+2/(x+1)^2
=(5x+5-4x-8)/(x+1)(x+2)+2/(x+1)^2
=5/(x+2)-4/(x+1)+2/(x+1)^2
2.(2x^2+x+2)/(x^3+1)
=(2x^2+x+2)/(x+1)(x^2-x+1)
=(x^2+2x+1+x^2-x+1)/(x+1)(x^2-x+1)
=(x+1)/(x^2-x+1)+1/(x+1)
=(x^2-2x-3+2x+4)/(x^2+1)^2(x+2)
=(x+1)(x-3)/(x+1)^2(x+2)+2(x+2)/(x+1)^2(x+2)
=(x-3)/(x+1)(x+2)+2/(x+1)^2
=(5x+5-4x-8)/(x+1)(x+2)+2/(x+1)^2
=5/(x+2)-4/(x+1)+2/(x+1)^2
2.(2x^2+x+2)/(x^3+1)
=(2x^2+x+2)/(x+1)(x^2-x+1)
=(x^2+2x+1+x^2-x+1)/(x+1)(x^2-x+1)
=(x+1)/(x^2-x+1)+1/(x+1)
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