Question

化简：[(x-4)/(x-2)]+[4/(x的平方-4x+4)]÷[x/x-2]

化简：[(x-4)/(x-2)]+[4/(x的平方-4x+4)]÷[x/x-2]
我最后得出的是 x的平方-4x+4
求正确步骤，（过程希望有的）

Answer 1

[(x-4)/(x-2)]+[4/(x的平方-4x+4)]÷[x/x-2]
=[(x-4)/(x-2)]+[4/(x-2)²]×（x-2）/x
=(x-4)/(x-2)+4/[x(x-2)]
=[x(x-4)+4]/[x(x-2)]
=[x²-4x+4]/[x(x-2)]
=(x-2)²/[x(x-2)]
=(x-2)/x

Answer 2

[(x-4)/(x-2)]+[4/(x的平方-4x+4)]÷[x/x-2]
=[(x-4)/(x-2)]+[4/(x的平方-4x+4)]*[(x-2)/x]
=[(x-4)/x+4/x(x-2)]
=(x^2-6x+12)/x(x-2)

Answer 3

(x-4)/(x-2)+[4/(x^2-4x+4)]÷[x/(x-2)]
(x-4)/(x-2)+4(x-2)/x(x-2)^2
(x-4)/(x-2)+4/x(x-2)
x(x-4)/x(x-2)+4/x(x-2)
[x(x-4)+4]/x(x-2)
(x^2-4x+4)/x(x-2)
(x-2)^2/x(x-2)
(x-2)/x