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\frac{\frac{s^{3}-8}{s-2}}{1}
Divide s^{2}-2s+4 by s^{2}-2s+4 to get 1.
\frac{\frac{\left(s-2\right)\left(s^{2}+2s+4\right)}{s-2}}{1}
Factor the expressions that are not already factored in \frac{s^{3}-8}{s-2}.
\frac{s^{2}+2s+4}{1}
Cancel out s-2 in both numerator and denominator.
s^{2}+2s+4
Anything divided by one gives itself.
\frac{\frac{s^{3}-8}{s-2}}{1}
Divide s^{2}-2s+4 by s^{2}-2s+4 to get 1.
\frac{\frac{\left(s-2\right)\left(s^{2}+2s+4\right)}{s-2}}{1}
Factor the expressions that are not already factored in \frac{s^{3}-8}{s-2}.
\frac{s^{2}+2s+4}{1}
Cancel out s-2 in both numerator and denominator.
s^{2}+2s+4
Anything divided by one gives itself.