来自孟颖悟的问题
【把分式(x+3)/[x(x^2-1)}化为部分分式】
把分式(x+3)/[x(x^2-1)}化为部分分式
(x+3)/[x(x^2-1)}
=[x(x^2-1)-x^3+2x+3]/[x(x^2-1)]
=1-(x^3-2x-3)/[x(x^2-1)]
=1-[(x^3-1)-(2x+2)]/[x(x^2-1)]
=1-[(x-1)(x^2+x+1)-2(x+1)]/[x(x+1)(x-1)]
=1-(x^2+x+1)/[x(x+1)]-2/[x(x-1)]
=1-[x(x+1)+1]/[x(x+1)]-2/[x(x-1)]
=1-1-1/[x(x+1)]-2/[x(x-1)]
=-[1/x-1/(x+1)]-2[1/(x-1)-1/x]
=-1/x+1/(x+1)-2/(x-1)+2/x
=1/x+1/(x+1)-2/(x-1)
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