To determine the numerator for the expression
[tex]\[
\frac{3}{k} + \frac{5}{k}
\][/tex]
we need to follow these steps:
1. Identify the fractions: We have two fractions, [tex]\(\frac{3}{k}\)[/tex] and [tex]\(\frac{5}{k}\)[/tex].
2. Common Denominator: Both fractions have the same denominator, [tex]\(k\)[/tex]. Since the denominators are identical, we can directly add the numerators.
3. Add the Numerators: Simply add the numerators of the two fractions.
[tex]\[
3 + 5
\][/tex]
Adding these two numbers gives us:
[tex]\[
3 + 5 = 8
\][/tex]
4. Form the New Fraction: The result of adding the numerators will be the numerator of the new fraction. So, we now have:
[tex]\[
\frac{8}{k}
\][/tex]
Thus, the numerator for the rational expression [tex]\(\frac{3}{k} + \frac{5}{k}\)[/tex] is [tex]\(8\)[/tex].
Finally, the expression can be rewritten as:
[tex]\[
\frac{3}{k} + \frac{5}{k} = \frac{8}{k}
\][/tex]
