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\frac{2\left(x-2\right)\left(x^{2}+\frac{5}{2}x+4\right)}{x-2}
Factor the expressions that are not already factored.
2\left(x^{2}+\frac{5}{2}x+4\right)
Cancel out x-2 in both numerator and denominator.
2x^{2}+5x+8
Expand the expression.
\frac{2\left(x-2\right)\left(x^{2}+\frac{5}{2}x+4\right)}{x-2}
Factor the expressions that are not already factored.
2\left(x^{2}+\frac{5}{2}x+4\right)
Cancel out x-2 in both numerator and denominator.
2x^{2}+5x+8
Expand the expression.