已知x>1 求(x^2-x+3)/(x-1)最小值（用均值不等式求）谢谢

题目

已知x>1 求(x^2-x+3)/(x-1)最小值（用均值不等式求）谢谢

答案

x>1则x-1>0
原式=(x²-x)/(x-1)+3/(x-1)
=x(x-1)/(x-1)+3/(x-1)
=x+3/(x-1)
=(x-1)+3/(x-1)+1≥2√[(x-1)*3/(x-1)]+1=2√3+1
所以最小值是2√3+1