<h3>
Answer:</h3>
5
<h3>
Step-by-step explanation:</h3>
Let n represent the numerator of the original fraction, which is n/(n+4). After adding 1/2, the value is (2(n+4)+1)/(2(n+4)), so we have ...
n/(n+4) + 1/2 = (2(n+4)+1)/(2(n+4))
Simplifying gives ...
... (2n +(n+4))/(2(n+4)) = (2n +9)/(2(n+4))
Since the denominators are the same, we can work only with the numerators.
3n +4 = 2n +9
n = 5 . . . . . . . . . . . subtract 2n+4
_____
<em>Check</em>
The original fraction is 5/(5+4) = 5/9. Adding 1/2 gives ...
5/9 + 1/2 = 10/18 + 9/18 = 19/18
Note the numerator of this last fraction is 1 more than the denominator, which is twice the original denominator.
