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# help with algebra

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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
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( 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
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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.

=$$\frac{1}{2}$$

Melody  Dec 5, 2020
#4
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thx :)

MobiusLoops  Dec 7, 2020
#2
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This occurs when:

a = 1   and    b = 9

Sum [1 + 9]== 10

Dec 4, 2020