2/(x-1)-2/(x+1)-1/(x-2)+1/(x+2)=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 13:35:41

2/(x-1)-2/(x+1)-1/(x-2)+1/(x+2)=?
2/(x-1)-2/(x+1)-1/(x-2)+1/(x+2)=?

2/(x-1)-2/(x+1)-1/(x-2)+1/(x+2)=?
2/(x-1)-2/(x+1)-1/(x-2)+1/(x+2)
=(2x+2-2x+2)/(x+1)(x-1)-(x+2-x+2)/(x+2)(x-2)
=4/(x+1)(x-1)-4/(x+2)(x-2)
=4(x²-4-x²+1)/(x+1)(x-1)(x+2)(x-2)
=-12/(x+1)(x-1)(x+2)(x-2)

或=-12/(x²-1)(x²-4)
=-12/(x^4-5x²+4)

答:
通分即可
原式
=2[x+1-(x-1)]/(x²-1)-[x+2-(x-2)]/(x²-4)
=4/(x²-1)-4/(x²-4)
=4[x²-4-(x²-1)]/[(x²-4)(x²-1)]
=-12/(x^4-5x²+4)

=2(x+1)-2(x-1))/(x+1)(x-1)+(-2(x+2)+2(x-2))/(x+2)(x-2)
=4(x2-4)-6(x2-1))/(x2-1)(x2-4)
=(-2(x2+5))/(x2-1)(x2-4)

-12/[(x-1)(x+1)(x-2)(x+2)]