求证1／（a-b）+1/(b-c)+1/(c-d)大于等于9/(a-d) (a>b>c>d)
我要详细的解题过程．谢谢！
參考答案:[1／（a-b）+1/(b-c)+1/(c-d)]*(a-d)
=[1／（a-b）+1/(b-c)+1/(c-d)]*(a-b+b-c+c-d)
=[a-b+b-c+c-d／（a-b）]+[a-b+b-c+c-d/(b-c)]+[a-b+b-c+c-d/(c-d)]
=3+(b-c/a-b)+(c-d/a-b)+(a-b/b-c)+(c-d/b-c)+(a-b/c-d)+(b-c/c-d)
=3+(b-c/a-b)+(a-b/b-c)+(c-d/a-b)+(a-b/c-d)+(b-c/c-d))+(c-d/b-c)
≥3+2+2+2=9
所以1／（a-b）+1/(b-c)+1/(c-d)大于等于9/(a-d) (a>b>c>d)