To find the sum of the given expressions, let's proceed step-by-step.
We need to add:
[tex]$
\frac{2x + 4}{(x + 1)} + \frac{-x + 5}{(x + 1)}
$[/tex]
1. Notice that both fractions have the same denominator, [tex]\( x + 1 \)[/tex]. When adding fractions with the same denominator, we can combine the numerators directly:
[tex]$
\frac{2x + 4}{x + 1} + \frac{-x + 5}{x + 1} = \frac{(2x + 4) + (-x + 5)}{x + 1}
$[/tex]
2. Combine the terms in the numerator:
[tex]$
(2x + 4) + (-x + 5) = 2x + 4 - x + 5
$[/tex]
Combine like terms:
[tex]$
2x - x + 4 + 5 = x + 9
$[/tex]
3. Now, the combined expression becomes:
[tex]$
\frac{x + 9}{x + 1}
$[/tex]
Hence, the sum is:
[tex]$
\frac{x + 9}{x + 1}
$[/tex]
Confirming from the given options, the correct one is:
[tex]$
\frac{x + 9}{x + 1}
$[/tex]
