Solve a^8+a^4+1/a^6-a^5+{a^3-a+1}+3-a-{a}^2

$$\frac{ { a }^{ 8 } + { a }^{ 4 } +1 }{ { a }^{ 6 } - { a }^{ 5 } + { a }^{ 3 } -a+1 } +3-a- { a }^{ 2 }$$

Evaluate

$$4$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{8}+a^{4}+1}{a^{6}-a^{5}+a^{3}-a+1}.

$$\frac{\left(a^{2}+a+1\right)\left(a^{2}-a+1\right)\left(a^{4}-a^{2}+1\right)}{\left(a^{2}-a+1\right)\left(a^{4}-a^{2}+1\right)}+3-a-a^{2}$$

Cancel out \left(a^{2}-a+1\right)\left(a^{4}-a^{2}+1\right) in both numerator and denominator.

$$a^{2}+a+1+3-a-a^{2}$$

Add 1 and 3 to get 4.

$$a^{2}+a+4-a-a^{2}$$

Combine a and -a to get 0.

$$a^{2}+4-a^{2}$$

Combine a^{2} and -a^{2} to get 0.

$$4$$

Factor

$$2^{2}$$