数学2次根式化简[x^2-x-2+(x-1)sqrt(x^2-4)]/[x^2+x-2+(x+1)sqrt(x^2-4)

来源：学生作业帮编辑：搜搜做题作业网作业帮分类：数学作业时间：2024/07/28 02:06:04

数学2次根式化简
[x^2-x-2+(x-1)sqrt(x^2-4)]/[x^2+x-2+(x+1)sqrt(x^2-4)] (x大于2)

原式=[(x-2)(x+1)+(x-1)sqrt(x+2)sqrt(x-2)]/[(x+2)(x-1)+(x+1)sqrt(x+2)sqrt(x-2)]
={sqrt(x-2)[(x+1)sqrt(x-2)+(x-1)sqrt(x+2)]}/{sqrt(x+2)[(x-1)sqrt(x+2)+(x+1)sqrt(x-2)]}
=sqrt(x-2)/sqrt(x+2)
=sqrt[(x-2)/(x+2)]

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