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\frac{3}{x+3}-\frac{2\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}
Factor the expressions that are not already factored in \frac{2x+4}{x^{2}+5x+6}.
\frac{3}{x+3}-\frac{2}{x+3}
Cancel out x+2 in both numerator and denominator.
\frac{1}{x+3}
Since \frac{3}{x+3} and \frac{2}{x+3} have the same denominator, subtract them by subtracting their numerators. Subtract 2 from 3 to get 1.
\frac{3}{x+3}-\frac{2\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}
Factor the expressions that are not already factored in \frac{2x+4}{x^{2}+5x+6}.
\frac{3}{x+3}-\frac{2}{x+3}
Cancel out x+2 in both numerator and denominator.
\frac{1}{x+3}
Since \frac{3}{x+3} and \frac{2}{x+3} have the same denominator, subtract them by subtracting their numerators. Subtract 2 from 3 to get 1.