化简分式，要完整的解题步骤
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a-4/2a+2
=a-2/a+2
=(a²-2+2a)/a
[1/(x²-2x)-1/(x²-4x+4)]÷2/(x²-2x)
=[1/x(x-2)-1/(x-2)²]÷2/(x²-2x)
=[(x-2-x)/x(x-2)²]÷2/x(x-2)
=[-2/x(x-2)²]÷2/x(x-2)
=-1/(x-2)
=1/(2-x)
[1-1/(x-1)]÷(x²-4x+4)/(x²-1)
=[(x-1-1)/(x-1)]÷[(x-2)²/(x-1)(x+1)]
=(x-2)/(x-1)÷[(x-2)²/(x-1)(x+1)]
=(x+1)/(x-2)
=a-2/a+2
=(a²-2+2a)/a
[1/(x²-2x)-1/(x²-4x+4)]÷2/(x²-2x)
=[1/x(x-2)-1/(x-2)²]÷2/(x²-2x)
=[(x-2-x)/x(x-2)²]÷2/x(x-2)
=[-2/x(x-2)²]÷2/x(x-2)
=-1/(x-2)
=1/(2-x)
[1-1/(x-1)]÷(x²-4x+4)/(x²-1)
=[(x-1-1)/(x-1)]÷[(x-2)²/(x-1)(x+1)]
=(x-2)/(x-1)÷[(x-2)²/(x-1)(x+1)]
=(x+1)/(x-2)
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