To solve the problem [tex]\(\frac{5}{x+2} + \frac{6}{x+4}\)[/tex], we need to combine these two fractions. In order to add fractions, they must have a common denominator. Here, the common denominator is [tex]\((x+2)(x+4)\)[/tex].
First, we rewrite each fraction with the common denominator:
[tex]\[
\frac{5}{x+2} = \frac{5(x+4)}{(x+2)(x+4)} = \frac{5x + 20}{(x+2)(x+4)}
\][/tex]
[tex]\[
\frac{6}{x+4} = \frac{6(x+2)}{(x+2)(x+4)} = \frac{6x + 12}{(x+2)(x+4)}
\][/tex]
Next, we add these two fractions:
[tex]\[
\frac{5x + 20}{(x+2)(x+4)} + \frac{6x + 12}{(x+2)(x+4)} = \frac{(5x + 20) + (6x + 12)}{(x+2)(x+4)}
\][/tex]
Combine the numerators:
[tex]\[
= \frac{5x + 6x + 20 + 12}{(x+2)(x+4)} = \frac{11x + 32}{(x+2)(x+4)}
\][/tex]
Therefore, the simplified form of [tex]\(\frac{5}{x+2} + \frac{6}{x+4}\)[/tex] is:
[tex]\[
\frac{11x + 32}{(x+2)(x+4)}
\][/tex]
The correct answer is:
C) [tex]\(\frac{11 x + 32}{(x+4)(x+2)}\)[/tex]
