作业帮化简分式[x/(x+1)-2/(x^2-1)]÷(x^2-4)/(x^2-2x+1)
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/11 02:26:29
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化简分式[x/(x+1)-2/(x^2-1)]÷(x^2-4)/(x^2-2x+1)
化简分式[x/(x+1)-2/(x^2-1)]÷(x^2-4)/(x^2-2x+1)
化简分式[x/(x+1)-2/(x^2-1)]÷(x^2-4)/(x^2-2x+1)
解
原式
=[x(x-1)/(x-1)(x+1)-2/(x+1)(x-1)]÷(x-2)(x+2)/(x-1)²
=[(x²-x-2)/(x-1)(x+1)]×(x-1)²/(x-2)(x+2)
=(x-2)(x+1)/(x-1)(x+1)×(x-1)²/(x-2)(x+2)
=(x-2)/(x-1)×(x-1)²/(x-2)(x+2)
=(x-1)/(x+2)
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