作业帮计算(x-2)/(x^2+3x+2)+6/(2+x-x^2-(x-10)/(x^2-4)
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/05/01 05:22:26
计算(x-2)/(x^2+3x+2)+6/(2+x-x^2-(x-10)/(x^2-4)
(x-2)/(x^2+3x+2)+6/(2+x-x^2)-(x-10)/(x^2-4)
=(x-2)/[(x+1)(x+2)]-6/[(x+1)(x-2)]-(x-10)/[(x-2)(x+2)]
=[(x-2)^2-6(x+2)-(x-10)(x+1)]/[(x-2)(x+1)(x+2)]
=[(x^2-4x+4)-(6x+12)-(x^2-9x-10)]/[(x-2)(x+1)(x+2)]
=[-x+2]/[(x-2)(x+1)(x+2)]
=-1/[(x+1)(x+2)]
=(x-2)/[(x+1)(x+2)]-6/[(x+1)(x-2)]-(x-10)/[(x-2)(x+2)]
=[(x-2)^2-6(x+2)-(x-10)(x+1)]/[(x-2)(x+1)(x+2)]
=[(x^2-4x+4)-(6x+12)-(x^2-9x-10)]/[(x-2)(x+1)(x+2)]
=[-x+2]/[(x-2)(x+1)(x+2)]
=-1/[(x+1)(x+2)]
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