Question 1164140
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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(unit)}}}   is excessive.

Mentioning that the numbers are fractions,  is excessive,  too.

The correct formulation is THIS :


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


In this formulation, the solution is as follows.



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


Then the condition says


    x - y = {{{(1/3)*(x + y)}}}.


Multiply both sides by 3 and simplify


    3x - 3y = x + y.

    3x - x = 3y + y

    2x     = 4y


It implies

    {{{x/y}}} = {{{4/2}}} = 2.


<U>ANSWER</U>.  Under the given conditions, the ratio of the larger number to the smaller is 2.
</pre>

Solved.


The post-solution note:


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

    The statement remains true in all these cases.
</pre>