作业帮计算：(x-1)/(x^2+3x+2)+6/(2+x-x^2)-(10-x)/(4-x^2)
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：2024/04/30 01:01:24
计算：(x-1)/(x^2+3x+2)+6/(2+x-x^2)-(10-x)/(4-x^2)
不好意思刚才那道弄错了 这道绝对没错
不好意思刚才那道弄错了 这道绝对没错
(x-1)/(x^2+3x-2)+6/(2+x-x^2)-(10-x)/(4-x^2)
=(x-1)/[(x+1)(x+2)]-6/[(x+1)(x-2)]-(x-10)/[(x+2)(x-2)]
=(x-1)(x-2)/[(x-2)(x+1)(x+2)]-6(x+2)/[(x+2)(x-1)(x-2)]-(x-10)/[(x-2)(x+2)]
=(x^2-3x+2-6x-12)/[(x-1)(x+2)(x-2)]-(x-10)/[(x-2)(x+2)]
=(x^2-9x-10)/[(x-1)(x-2)(x+2)]-(x-10)/[(x-2)(x+2)]
=(x+1)(x-10)/[(x-1)(x+2)(x-2)]-(x-10)(x-1)/[(x-1)(x+2)(x-2)]
=(x-10)(x+1-x+1)/[(x-1)(x+2)(x-2)]
=2(x-10)/[(x-1)(x+2)(x-2)]
=(x-1)/[(x+1)(x+2)]-6/[(x+1)(x-2)]-(x-10)/[(x+2)(x-2)]
=(x-1)(x-2)/[(x-2)(x+1)(x+2)]-6(x+2)/[(x+2)(x-1)(x-2)]-(x-10)/[(x-2)(x+2)]
=(x^2-3x+2-6x-12)/[(x-1)(x+2)(x-2)]-(x-10)/[(x-2)(x+2)]
=(x^2-9x-10)/[(x-1)(x-2)(x+2)]-(x-10)/[(x-2)(x+2)]
=(x+1)(x-10)/[(x-1)(x+2)(x-2)]-(x-10)(x-1)/[(x-1)(x+2)(x-2)]
=(x-10)(x+1-x+1)/[(x-1)(x+2)(x-2)]
=2(x-10)/[(x-1)(x+2)(x-2)]
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