Solve x^4-x^3+x-1/x^2-x+1

$$x ^ { 4 } - x ^ { 3 } + x - 1 / x ^ { 2 } - x + 1$$

Evaluate

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

Short Solution Steps

Combine x and -x to get 0.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{4}-x^{3}+1 times \frac{x^{2}}{x^{2}}.

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

Since \frac{\left(x^{4}-x^{3}+1\right)x^{2}}{x^{2}} and \frac{1}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(x^{4}-x^{3}+1\right)x^{2}-1.

$$\frac{x^{6}-x^{5}+x^{2}-1}{x^{2}}$$

Factor

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