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\frac{x+4}{x^{2}+6x+8}
Since \frac{x}{x^{2}+6x+8} and \frac{4}{x^{2}+6x+8} have the same denominator, add them by adding their numerators.
\frac{x+4}{\left(x+2\right)\left(x+4\right)}
Factor the expressions that are not already factored in \frac{x+4}{x^{2}+6x+8}.
\frac{1}{x+2}
Cancel out x+4 in both numerator and denominator.