Evaluate
a^{3}+4a+\frac{16}{a}
Expand
a^{3}+4a+\frac{16}{a}
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\frac{\left(a^{3}-8\right)\left(a^{3}+8\right)}{\left(a^{2}-4\right)a}
Divide \frac{a^{3}-8}{a^{2}-4} by \frac{a}{a^{3}+8} by multiplying \frac{a^{3}-8}{a^{2}-4} by the reciprocal of \frac{a}{a^{3}+8}.
\frac{\left(a-2\right)\left(a+2\right)\left(a^{2}-2a+4\right)\left(a^{2}+2a+4\right)}{a\left(a-2\right)\left(a+2\right)}
Factor the expressions that are not already factored.
\frac{\left(a^{2}-2a+4\right)\left(a^{2}+2a+4\right)}{a}
Cancel out \left(a-2\right)\left(a+2\right) in both numerator and denominator.
\frac{a^{4}+4a^{2}+16}{a}
Expand the expression.
\frac{\left(a^{3}-8\right)\left(a^{3}+8\right)}{\left(a^{2}-4\right)a}
Divide \frac{a^{3}-8}{a^{2}-4} by \frac{a}{a^{3}+8} by multiplying \frac{a^{3}-8}{a^{2}-4} by the reciprocal of \frac{a}{a^{3}+8}.
\frac{\left(a-2\right)\left(a+2\right)\left(a^{2}-2a+4\right)\left(a^{2}+2a+4\right)}{a\left(a-2\right)\left(a+2\right)}
Factor the expressions that are not already factored.
\frac{\left(a^{2}-2a+4\right)\left(a^{2}+2a+4\right)}{a}
Cancel out \left(a-2\right)\left(a+2\right) in both numerator and denominator.
\frac{a^{4}+4a^{2}+16}{a}
Expand the expression.
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Limits
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