SOLUTION: The difference of two unit fractions is one third of their sum. Find ratio of the larger fraction to smaller fraction ....A fraction sum ..

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Question 1164140: The difference of two unit fractions is one third of their sum. Find ratio of the larger fraction to smaller fraction ....A fraction sum ..
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Let (1/a) > (1/b)

+%281%2Fa%29+-+%281%2Fb%29+=+%281%2F3%29%28%281%2Fa%29+%2B+%281%2Fb%29%29+

++%283%2Fa%29+-+%283%2Fb%29+=+%281%2Fa%29+%2B+%281%2Fb%29+

++%282%2Fa%29+=+%284%2Fb%29+ ... subtracted 1/a & added 3/b to both sides

++%28%281%2Fa%29%29%2F%28%281%2Fb%29%29+=+2+

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
The difference of two unit fractions is one third of their sum. Find ratio of the larger fraction to smaller fraction ....A fraction sum ..
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In this problem, the word  highlight%28unit%29  is excessive.
Mentioning that the numbers are fractions,  is excessive,  too.
The correct formulation is THIS : 

    The difference of two numbers is one third of their sum. 
    Find the ratio of the larger number to the smaller one.


In this formulation, the solution is as follows. 


Let x be the greater number, while "y" be the smaller number.


Then the condition says


    x - y = %281%2F3%29%2A%28x+%2B+y%29.


Multiply both sides by 3 and simplify


    3x - 3y = x + y.

    3x - x = 3y + y

    2x     = 4y


It implies

    x%2Fy = 4%2F2 = 2.


ANSWER.  Under the given conditions, the ratio of the larger number to the smaller is 2.

Solved.

The post-solution note: 

    The numbers can be rational, irrational, algebraic, transcendent, and even complex.

    The statement remains true in all these cases.