Question 1204643
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The denominator of a fraction is 7 more than the numerator. If both the numerator and the denominator 
are decreased by 2​, the resulting fraction is equivalent to 6/13. Find the fraction.
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<pre>
Let x be the numerator of the original fraction.
Then the denominator is (x+7).


From the condition, we have this equation

    {{{(x-2)/((x+7)-2)}}} = {{{6/13}}}.


Simplify and find x

    {{{(x-2)/(x+5)}}} = {{{6/13}}}

    13(x-2) = 6(x+5)

    13x - 26 = 6x + 30

    13x - 6x = 30 + 26

        7x   =   56.

         x   =   56/7 = 8.


<U>ANSWER</U>.  The fraction is  {{{8/15}}}.
</pre>

Solved.