To add the given fractions, follow these steps:
1. Identify Common Denominator:
Both fractions \(\frac{3}{4x^5}\) and \(\frac{5}{4x^5}\) already have the same denominator, which is \(4x^5\).
2. Add the Numerators:
Since the denominators are the same, we can directly add the numerators:
[tex]\[
\frac{3}{4x^5} + \frac{5}{4x^5} = \frac{3 + 5}{4x^5}
\][/tex]
3. Combine the Numerators:
Simplify the numerator by adding together:
[tex]\[
3 + 5 = 8
\][/tex]
4. Form the Resulting Fraction:
Using the simplified numerator, we form the final fraction:
[tex]\[
\frac{8}{4x^5}
\][/tex]
5. Simplify the Fraction:
We can simplify the fraction by dividing both the numerator and the denominator by the common factor \(4\):
[tex]\[
\frac{8 \div 4}{4x^5 \div 4} = \frac{2}{x^5}
\][/tex]
Thus, the simplified form of the given expression is:
[tex]\[
\boxed{\frac{2}{x^5}}
\][/tex]
