作业帮化简[(x+1)/(x^2-3x+2)]+[x/(2x^2-x-1)]-[(x-1)/(2x^2-3x-2)]
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/04/29 04:18:50
化简[(x+1)/(x^2-3x+2)]+[x/(2x^2-x-1)]-[(x-1)/(2x^2-3x-2)]
[(x+1)/(x^2-3x+2)]+[x/(2x^2-x-1)]-[(x-1)/(2x^2-3x-2)]
=(x+1)/[(x-2)(x-1)]+x/[(2x+1)(x-1)]-(x-1)/[(2x+1)(x-2)]
=(x+1)/[(x-2)(x-1)]+[x(x-2)-(x-1)^2]/[(2x+1)(x-1)(x-2)]
=[(x+1)(2x+1)-1]/[(2x+1)(x-1)(x-2)]
=(2x^2+3x+1-1)/[(2x+1)(x-1)(x-2)]
=x(2x+3)/[(2x+1)(x-1)(x-2)]
=(x+1)/[(x-2)(x-1)]+x/[(2x+1)(x-1)]-(x-1)/[(2x+1)(x-2)]
=(x+1)/[(x-2)(x-1)]+[x(x-2)-(x-1)^2]/[(2x+1)(x-1)(x-2)]
=[(x+1)(2x+1)-1]/[(2x+1)(x-1)(x-2)]
=(2x^2+3x+1-1)/[(2x+1)(x-1)(x-2)]
=x(2x+3)/[(2x+1)(x-1)(x-2)]
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