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\frac{b^{2}-4}{b+2}
Since \frac{b^{2}}{b+2} and \frac{4}{b+2} have the same denominator, subtract them by subtracting their numerators.
\frac{\left(b-2\right)\left(b+2\right)}{b+2}
Factor the expressions that are not already factored in \frac{b^{2}-4}{b+2}.
b-2
Cancel out b+2 in both numerator and denominator.