Hi,

Let x represent  and y the other

the difference of their reciprocals is 3

1/y - (1/x)= 3 

Multiplying thru with xy to clear the demominators

x - y  = 3xy

the sum of two numbers is the same as their product****

x + y = xy

Adding the equation together & eliminating the y variable

2x = 4xy

1/2 = y

substituting for y 

x + 1/2 = x/2

x/2 = -1/2

x = -1

Checking our answer

 2 - (-1) = 3 

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