Question 1207709
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0 < a < b
a < b
a*(1/a) < b*(1/a)
1 < b/a
1*(1/b) < (b/a)*(1/b)
1/b < 1/a
0 < 1/b < 1/a


Since a > 0, we know that 1/a > 0 also.
Multiplying both sides by a positive number will not flip the inequality sign.
The same applies for b as well. 
b > 0 leads to 1/b > 0.


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Another approach


0 < a < b
a < b
a*(1/(ab)) < b*(1/(ab))
1/b < 1/a
0 < 1/b < 1/a


Note that a > 0 and b > 0 lead to ab > 0, and furthermore 1/(ab) > 0.
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