Question

Add the following rational expressions: 2x+1/x+4+ x−5/x+4. Enter each response with terms arranged in order from largest degree to smallest degree.(1 point)

Answer 1

To add the rational expressions \(\frac{2x + 1}{x + 4}\) and \(\frac{x - 5}{x + 4}\), we need a common denominator. Since both fractions have the same denominator, we can directly add the numerators.

The expression can be rewritten as:

\[
\frac{2x + 1 + (x - 5)}{x + 4}
\]

Now combine the numerators:

\[
2x + 1 + x - 5 = 2x + x + 1 - 5 = 3x - 4
\]

Now we can write the combined expression:

\[
\frac{3x - 4}{x + 4}
\]

So, the final result of adding the two rational expressions is:

\[
\frac{3x - 4}{x + 4}
\]

This is the answer with terms arranged in order from largest degree to smallest degree.