Question 1087819
Let the numerator = x
So the denominator = x+2

So the fraction = {{{x/(x+2)}}}   ....  ......  ..... (1)
As per the condition,

{{{(x*4)/(x+2+8) = 4/3}}}

{{{ 4x/(x+10) = 4/3}}}

By cross-multiplying the equation,

{{{12x  = 4*(x+10)}}}

{{{12x = 4x+40}}}

Subtracting 4x both the sides,

{{{12x-4x = 4x-4x+40}}}

{{{8x = 40}}}

{{{x = 40/8 = 5;  x = 5}}}

Replacing the value of x in (1),

{{{x/(x+2) = 5/7}}}

The original rational number = {{{5/7}}}.  Answer. 

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