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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Expand

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

Short Solution Steps

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

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

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

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

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

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