Solve x^4-2x^2+1divx-1

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

$$\frac{x^{5}-2x^{3}-x+1}{x}$$

Factor

$$\frac{\left(x-\frac{-\sqrt{5}-1}{2}\right)\left(x-\frac{\sqrt{5}-1}{2}\right)\left(x^{3}-x^{2}-1\right)}{x}$$