Solve x^5+x^4+x^2+1/x^2+1

$$x ^ { 5 } + x ^ { 4 } + x ^ { 2 } + 1 / x ^ { 2 } + 1$$

Evaluate

$$x^{5}+x^{4}+x^{2}+1+\frac{1}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{5}+x^{4}+x^{2}+1 times \frac{x^{2}}{x^{2}}.

$$\frac{\left(x^{5}+x^{4}+x^{2}+1\right)x^{2}}{x^{2}}+\frac{1}{x^{2}}$$

Since \frac{\left(x^{5}+x^{4}+x^{2}+1\right)x^{2}}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{5}+x^{4}+x^{2}+1\right)x^{2}+1}{x^{2}}$$

Do the multiplications in \left(x^{5}+x^{4}+x^{2}+1\right)x^{2}+1.

$$\frac{x^{7}+x^{6}+x^{4}+x^{2}+1}{x^{2}}$$

Factor

$$\frac{x^{7}+x^{6}+x^{4}+x^{2}+1}{x^{2}}$$