6x+12x+10/x+2x+2=6（x+2x+2)-2/x+2x+2=6-2/x+2x+2=6-2/(x+1）+1,又因为(x+1）+1属于1到正无穷,所以2/(x+1）+1属于0到2（0取不到,2取到）,所以原式最小值为4,希望能给你帮助.