Solve a^4-a^2-2a-1diva^2+a+1

$$a ^ { 4 } - a ^ { 2 } - 2 a - 1 \div a ^ { 2 } + a + 1$$

Evaluate

$$a^{4}-a^{2}-a+1-\frac{1}{a^{2}}$$

Short Solution Steps

Combine -2a and a to get -a.

$$a^{4}-a^{2}-a-\frac{1}{a^{2}}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a^{4}-a^{2}-a+1 times \frac{a^{2}}{a^{2}}.

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

Since \frac{\left(a^{4}-a^{2}-a+1\right)a^{2}}{a^{2}} and \frac{1}{a^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(a^{4}-a^{2}-a+1\right)a^{2}-1.

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

Factor

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