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What is the sum?

[tex]\[
\frac{2x+4}{x+1} + \frac{-x+5}{x+1}
\][/tex]

A. [tex]\(\frac{x-1}{x+1}\)[/tex]

B. [tex]\(\frac{x-1}{2x+2}\)[/tex]

C. [tex]\(\frac{x+9}{x+1}\)[/tex]

D. [tex]\(\frac{x+9}{2x+2}\)[/tex]


Sagot :

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]