Solve x^2-2x(x-1/x)+x1/x^2

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{xx}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in xx-1.

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

Express 2\times \frac{x^{2}-1}{x} as a single fraction.

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

Express x\times \frac{1}{x^{2}} as a single fraction.

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

Cancel out x in both numerator and denominator.

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

Use the distributive property to multiply 2 by x^{2}-1.

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

Cancel out x and x.

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

To find the opposite of 2x^{2}-2, find the opposite of each term.

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

Combine x^{2} and -2x^{2} to get -x^{2}.

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

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

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

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

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

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

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

Expand

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

Short Solution Steps

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

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

Since \frac{xx}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in xx-1.

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

Express 2\times \frac{x^{2}-1}{x} as a single fraction.

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

Express x\times \frac{1}{x^{2}} as a single fraction.

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

Cancel out x in both numerator and denominator.

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

Use the distributive property to multiply 2 by x^{2}-1.

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

Cancel out x and x.

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

To find the opposite of 2x^{2}-2, find the opposite of each term.

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

Combine x^{2} and -2x^{2} to get -x^{2}.

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

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

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

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

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

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

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