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When the sum of the reciprocals of two distinct positive integers is divided by the sum of the two integers, the result is 1/9. What is the sum of the two integers?

 Dec 4, 2020
 #1
avatar+277 
+2

( 1/a + 1/b)             1

_________  =       ___

      a+b                  9

 

 

        [a+b]

      ______

        [ab]                      1

___________     =    ____    

                                     9

         a+b

 

 

           1                      1

   _________    =  ______

            ab                   9

 

            ab=9

 

Two distinct numbers

 

9 and 1

 

9+1 or 1+9

 

Both are equal to 10

 

 

sorry if I was unclear. I'm not good at latex

 Dec 4, 2020
edited by MobiusLoops  Dec 4, 2020
 #3
avatar+112086 
+1

Your answer is very clear.  laugh

 

 

If you want help with Latex this is a good site to start on.  What you have written would not be terribly difficult in LaTex but to start,

the fraction 1/2   is just

 

\frac{1}{2}

 

\frac means that what follows is to be written as a fraction.   

The numerator goes in the first set of parentheses and the denominator goes in the second set.

 

Easy peazy.

 

=\(\frac{1}{2}\)

Melody  Dec 5, 2020
 #4
avatar+277 
+1

thx :)

MobiusLoops  Dec 7, 2020
 #2
avatar
0

This occurs when:

 

a = 1   and    b = 9

 

Sum [1 + 9]== 10

 Dec 4, 2020

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