Final answer:
To add the fractions with the same denominator (4x), we combine the numerators to get 10/4x, then simplify by dividing both numerator and denominator by 2, resulting in the simplified fraction 5/2x.
Step-by-step explanation:
To add the fractions ⅛ (1/4x) + ⅓ (9/4x), we need to ensure that they have the same denominator, which they do in this case, both being 4x. When adding fractions with the same denominator, we combine the numerators and keep the common denominator the same:
1/4x + 9/4x = (1 + 9) / 4x = 10 / 4x
Now, we simplify the fraction if possible. In this case, both the numerator and denominator are divisible by 2, which simplifies the fraction to:
10 / 4x = 5 / 2x
This is the simplified form of the added fractions.