The sum of the numerator and the denominator

Here we are assuming that numerator and denominator are $x$ and $y$ respectively, then fraction will be $\frac{x}{y}$ and we have to find the value of $\frac{x}{y}$.

From the given condition,

x + y = 8…… (1)

If 3 are added in numerator and denominator then fraction will be $\frac{3}{4}$, from this we have

$\frac{x+3}{y+3}=\frac{3}{4}$

Now, multiply the equation (1) by 3, we get

3x + 3y = 24…… (3)

Now we take the addition of equations (2) and (3), we get

$7 x=21$

$\Rightarrow x=3$

Put the value of x in the equation (1), we have

$3+y=8$

$\Rightarrow y=5$

Hence the fraction is $\frac{x}{y}=\frac{3}{5}$