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The Nature of Mathematical Inequalities in Senior High School
Solution:

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 ~