Let's solve the problem step-by-step to identify the correct expression.
1. Determine the numerator:
We need to find the sum of [tex]\(2x\)[/tex] and [tex]\(5y\)[/tex]. This gives us:
[tex]\[
\text{Numerator} = 2x + 5y
\][/tex]
2. Determine the denominator:
We need to find the product of [tex]\(2x\)[/tex] and 8. This gives us:
[tex]\[
\text{Denominator} = 2x \cdot 8 = 16x
\][/tex]
3. Form the initial expression:
Combine the numerator and the denominator to form the initial fraction:
[tex]\[
\text{Expression} = \frac{2x + 5y}{16x}
\][/tex]
4. Simplify the expression:
We check if the expression [tex]\(\frac{2x + 5y}{16x}\)[/tex] can be simplified further. In this case, the expression is already in its simplest form when written out, as there are no common factors to factor out from the numerator and the denominator together.
5. Compare to the given options:
- Option A: [tex]\(2 x + 5 y\)[/tex]
- Option B: [tex]\(\frac{5 y}{8}\)[/tex]
- Option C: [tex]\(\frac{2 x + 5 y}{8}\)[/tex]
- Option D: [tex]\(2 x + \frac{5 y}{16 x}\)[/tex]
- Option E: [tex]\(\frac{2 x + 5 y}{16 x}\)[/tex]
The simplified expression [tex]\(\frac{2x + 5y}{16x}\)[/tex] corresponds to option E.
Therefore, the correct answer is:
[tex]\[
\boxed{E \ \frac{2 x + 5 y}{16 x}}
\][/tex]
