7. 1/(a-b)- 1/a
=b/a(a-b)
a & ltb & lt0
a-b & lt; 0
∴ 1/(a-b)- 1/a<; 0
∴ 1/(a-b)<; 1/a
8.(a/√b+b/√a)-(√a+√b)
=(a-b)(√a-√b)/√ab
A-b and √a-√b are both positive and negative, or 0 when a = b.
Ⅷ above formula 0
∴a/√b+b/√a≥√a+√b
9.f(a)=ma/(a- 1),f(b)=mb/(b- 1)
f(a)-f(b)= m(b-a)/[(a- 1)(b- 1)]
∵a & gt; b & gt 1
∴b-a<; 0a- 1 & gt; 0 b- 1 & gt; 0
∴f(a)-f(b)<; 0
f(a)& lt; f(b)
Finish it carefully, I hope it will help you ~