Let the denominator of the first fraction be $x$. Since the numerator is 3 less than the denominator, the numerator of the first fraction is $x - 3$. Therefore, the first fraction is:

$\frac{x - 3}{x}$

For the second fraction, the numerator is multiplied by 2, so the new numerator becomes $2(x - 3)$. The denominator of the second fraction has 4 added to it, so the new denominator becomes $x + 4$. The second fraction is:

$\frac{2(x - 3)}{x + 4}$

We are told that the sum of the two fractions is $\frac{1}{2}$. Therefore, the equation becomes:

$\frac{x - 3}{x} + \frac{2(x - 3)}{x + 4} = \frac{1}{2}$

This is the equation in terms of $x$.

Would you like details on how to solve this equation? Here are 5 related questions:

1. How do you solve a rational equation like this one?
2. Can you simplify the expressions further before solving?
3. What happens if the denominator $x$ is a specific value?
4. Can this type of problem appear in algebraic fractions?
5. What is the significance of checking for restrictions on $x$?

Tip: When adding fractions, always find a common denominator first to combine them properly.