Let smaller number be S

Then larger is: 

Smaller number's reciprocal: 

Larger number's reciprocal:  , or 

Difference of their reciprocals equals , so: 

 ----- Multiplying by LCD, 6S



(2S - 3)(S + 2) = 0

2S = 3                OR             S + 2 = 0

S, or smaller number = 



If smaller number is: , then larger number is: , or , or 2. 

Thus, numbers CAN BE: 



If smaller number is: , then larger number is: , or  

Thus, numbers CAN BE:  

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