To add the rational expressions [tex]\(\frac{8w + 6}{w - 4}\)[/tex] and [tex]\(\frac{3w + 8}{w - 4}\)[/tex], follow these steps:
1. Ensure a Common Denominator:
Both expressions have the same denominator, [tex]\(w - 4\)[/tex]. Thus, we can directly add the numerators while keeping the common denominator.
2. Add the Numerators:
Combine the numerators [tex]\((8w + 6)\)[/tex] and [tex]\((3w + 8)\)[/tex]:
[tex]\[
\frac{8w + 6}{w - 4} + \frac{3w + 8}{w - 4} = \frac{(8w + 6) + (3w + 8)}{w - 4}
\][/tex]
3. Combine Like Terms:
Add the like terms in the numerator:
[tex]\[
(8w + 3w) + (6 + 8) = 11w + 14
\][/tex]
4. Rewrite the Expression:
The combined numerator is [tex]\(11w + 14\)[/tex]. Therefore, we have:
[tex]\[
\frac{8w + 6}{w - 4} + \frac{3w + 8}{w - 4} = \frac{11w + 14}{w - 4}
\][/tex]
So the simplified answer is:
[tex]\[
\frac{11w + 14}{w - 4}
\][/tex]
Thus, the final simplified form of the given rational expressions is [tex]\(\frac{11w + 14}{w - 4}\)[/tex].
