搜搜考试网因式分解: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 编辑：搜搜考试网作业帮 分类：数学作业 时间：2024/07/15 19:42:26
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+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)