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?
+505 ( 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
+118677 Your answer is very clear. 
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.
=\(\frac{1}{2}\)
