求式子的取值范围(用基本不等式)x^2-3x+3/x-2(x>2)

问题描述:

求式子的取值范围(用基本不等式)x^2-3x+3/x-2(x>2)

(x²-3x+3)/(x-2)
=(x²-2x-x+2+1)/(x-2)
=x-1+1/(x-2)
=(x-2)+1/(x-2)+1
>=2+1=3
∴(x^2-3x+3)/(x-2)>=3 (x>2)=(x²-2x-x+2+1)/(x-2)是怎么转化成x-1+1/(x-2)的啊??x²-2x-x+2+1=x(x-2)-(x-2)+1