To find the sum of the rational expressions [tex]\(\frac{3}{5x} + \frac{8}{5x}\)[/tex], follow these steps:
1. Identify the Common Denominator:
Both fractions have the same denominator, [tex]\(5x\)[/tex].
2. Add the Numerators:
Since the denominators are the same, simply add the numerators together:
[tex]\[
\frac{3}{5x} + \frac{8}{5x} = \frac{3 + 8}{5x}
\][/tex]
3. Simplify the Numerator:
Calculate the sum of the numerators:
[tex]\[
3 + 8 = 11
\][/tex]
4. Write the Resulting Fraction:
Place the sum of the numerators over the common denominator:
[tex]\[
\frac{11}{5x}
\][/tex]
5. Verify the Answer among the Given Choices:
The correct answer matches option D:
[tex]\[
\frac{11}{5x}
\][/tex]
Therefore, the sum of the rational expressions is:
[tex]\[
\boxed{\frac{11}{5x}}
\][/tex]
Hence, the correct answer is option D: [tex]\(\frac{11}{5x}\)[/tex].
