因式分解:1/(x平方-1)+1/(x平方+4x+3)+1/(x平方+8x+15)+1/(x平方+12x+35)

来源：学生作业帮助网编辑：作业帮时间：2024/05/12 18:41:18

因式分解:1/(x平方-1)+1/(x平方+4x+3)+1/(x平方+8x+15)+1/(x平方+12x+35)
因式分解:1/(x平方-1)+1/(x平方+4x+3)+1/(x平方+8x+15)+1/(x平方+12x+35)

因式分解:1/(x平方-1)+1/(x平方+4x+3)+1/(x平方+8x+15)+1/(x平方+12x+35)
1/(x平方-1)+1/(x平方+4x+3)+1/(x平方+8x+15)+1/(x平方+12x+35)
=1/(x+1)(x-1)+1/(x+1)(x+3)+1/(x+3)(x+5)+1/(x+5)(x+7)
=1/2{1/(x-1)-1/(x+1)}+1/2{1/(x+1)-1/(x+3)}+1/2{1/(x+3)-1/(x+5)}+1/2{1/(x+5)-1/(x+7)}
=1/2{1/(x-1)-1/(x+7)}
=1/2(x+7-x+1)/(x-1)(x+7)
=4/(x-1)(x+7)

1/(x平方-1)+1/(x平方+4x+3)+1/(x平方+8x+15)+1/(x平方+12x+35)
=1/(x+1)(x-1)+1/(x+1)(x+3)+1/(x+3)(x+5)+1/(x+5)(x+7)
=1/2{1/(x-1)-1/(x+1)}+1/2{1/(x+1)-1/(x+3)}+1/2{1/(x+3)-1/(x+5)}+1/2{1/(x+5)-1/(x+7)}
=1/2{1/(x-1)-1/(x+7)}
=1/2(x+7-x+1)/(x-1)(x+7)
=4/(x-1)(x+7)

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