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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and x is x^{2}. Multiply \frac{2}{x} times \frac{x}{x}.

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

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

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

Factor

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