∵x>3
∴1/(x-3)>0,x-3>0
∴(x-3)+1/(x-3)+3≥2√(x-3)*[1/(x-3)]+3=2+3=5
当x-3=1/(x-3)时,取等号,(x-3)+1/(x-3)+3有最小值5
即x+1/(x-3)有最小值5