To multiply powers of the same base, add their exponents. Add $3$ and $4$ to get $7$.
$$factor(a^{7}+\frac{a^{4}}{a^{3}})$$
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract $3$ from $4$ to get $1$.
$$factor(a^{7}+a^{1})$$
Calculate $a$ to the power of $1$ and get $a$.
$$factor(a^{7}+a)$$
Factor out $a$.
$$a\left(a^{6}+1\right)$$
Consider $a^{6}+1$. Rewrite $a^{6}+1$ as $\left(a^{2}\right)^{3}+1^{3}$. The sum of cubes can be factored using the rule: $p^{3}+q^{3}=\left(p+q\right)\left(p^{2}-pq+q^{2}\right)$.
Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: $a^{4}-a^{2}+1,a^{2}+1$.
