15问答网 > 分式化简：[(x+2)⼀(x^2-2x)-(x-1)⼀(x^2-4x+4)]⼀(x-4)⼀(x^3-2x^2)

分式化简：[(x+2)⼀(x^2-2x)-(x-1)⼀(x^2-4x+4)]⼀(x-4)⼀(x^3-2x^2)

分式化简：[(x+2)/(x^2-2x)-(x-1)/(x^2-4x+4)]/(x-4)/(x^3-2x^2)

2025-05-23 07:51:12

推荐回答（4个）

回答1：

x/(x-2)

附图:

回答2：

[(x+2)/(x^2-2x)-(x-1)/(x^2-4x+4)]/(x-4)/(x^3-2x^2)
=(x+2)x^2(x-2)/[x(x-2)(x-4)]-(x-1)x^2(x-2)/[(x-2)^2(x-4)]
=(x+2)x/(x-4)-(x-1)x^2/[(x-2)(x-4)]
=(x^3-4x-x^3+x^2)/[(x-2)(x-4)]
=x(x-4)/[(x-2)(x-4)]
=x/(x-2)

回答3：

[(x+2)/(x^2-2x)-(x-1)/(x^2-4x+4)]/[(x-4)/(x^3-2x^2)]
=[(x+2)/x(x-2)-(x-1)/(x-2)^2]/[(x-4)/x^2(x-2)]
={[(x+2)(x-2)-x(x-1)]/x(x-2)^2}/[(x-4)/x^2(x-2)]
=[(x^2-4-x^2+x)/(x-2)]/[(x-4)/x]
=[(x-4)/(x-2)]/[(x-4)/x]
=x/(x-2)

回答4：

x/(x-2)