To add the two fractions, we first need to find a common denominator. The common denominator for 2 and 4 is 4. So, we can rewrite the fractions as follows:
1/2 (x+4) = 2/4 (x+4)
1/4 (4x−2) = 1/4 * 1 * (4x-2) = 1/4 * 4x - 1/4 * 2 = 4/4 x - 1/2
Now we can add the fractions:
2/4 (x+4) + 4/4 x - 1/2
Combining the x terms, we have:
(2/4 + 4/4) x + 4/4
Simplifying the fractions, we get:
6/4 x + 4/4
Now, we can separate the whole number part and the fractional part:
6/4 x can be simplified to 3/2 x, and 4/4 can be simplified to 1. So, the final answer is:
3/2 x + 1 (in mixed number form)