Evaluate
x^{3}+3x^{2}-8-\frac{12}{x}
Expand
x^{3}+3x^{2}-8-\frac{12}{x}
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\frac{x\left(x-2\right)\left(x+3\right)\left(x^{2}+2x+2\right)}{x^{2}}+2x+2
Factor the expressions that are not already factored in \frac{x^{5}+3x^{4}-2x^{3}-10x^{2}-12x}{x^{2}}.
\frac{\left(x-2\right)\left(x+3\right)\left(x^{2}+2x+2\right)}{x}+2x+2
Cancel out x in both numerator and denominator.
\frac{\left(x-2\right)\left(x+3\right)\left(x^{2}+2x+2\right)}{x}+\frac{\left(2x+2\right)x}{x}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2x+2 times \frac{x}{x}.
\frac{\left(x-2\right)\left(x+3\right)\left(x^{2}+2x+2\right)+\left(2x+2\right)x}{x}
Since \frac{\left(x-2\right)\left(x+3\right)\left(x^{2}+2x+2\right)}{x} and \frac{\left(2x+2\right)x}{x} have the same denominator, add them by adding their numerators.
\frac{x^{4}+5x^{3}+8x^{2}+6x-2x^{3}-10x^{2}-16x-12+2x^{2}+2x}{x}
Do the multiplications in \left(x-2\right)\left(x+3\right)\left(x^{2}+2x+2\right)+\left(2x+2\right)x.
\frac{x^{4}+3x^{3}-8x-12}{x}
Combine like terms in x^{4}+5x^{3}+8x^{2}+6x-2x^{3}-10x^{2}-16x-12+2x^{2}+2x.
\frac{x\left(x-2\right)\left(x+3\right)\left(x^{2}+2x+2\right)}{x^{2}}+2x+2
Factor the expressions that are not already factored in \frac{x^{5}+3x^{4}-2x^{3}-10x^{2}-12x}{x^{2}}.
\frac{\left(x-2\right)\left(x+3\right)\left(x^{2}+2x+2\right)}{x}+2x+2
Cancel out x in both numerator and denominator.
\frac{\left(x-2\right)\left(x+3\right)\left(x^{2}+2x+2\right)}{x}+\frac{\left(2x+2\right)x}{x}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2x+2 times \frac{x}{x}.
\frac{\left(x-2\right)\left(x+3\right)\left(x^{2}+2x+2\right)+\left(2x+2\right)x}{x}
Since \frac{\left(x-2\right)\left(x+3\right)\left(x^{2}+2x+2\right)}{x} and \frac{\left(2x+2\right)x}{x} have the same denominator, add them by adding their numerators.
\frac{x^{4}+5x^{3}+8x^{2}+6x-2x^{3}-10x^{2}-16x-12+2x^{2}+2x}{x}
Do the multiplications in \left(x-2\right)\left(x+3\right)\left(x^{2}+2x+2\right)+\left(2x+2\right)x.
\frac{x^{4}+3x^{3}-8x-12}{x}
Combine like terms in x^{4}+5x^{3}+8x^{2}+6x-2x^{3}-10x^{2}-16x-12+2x^{2}+2x.
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