Solve =(1/x)^2+2x1/x*x+x^3

$$= ( \frac { 1 } { x } ) ^ { 2 } + 2 x \frac { 1 } { x } \times x + x ^ { 3 }$$

Evaluate

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

Short Solution Steps

Multiply x and x to get x^{2}.

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

To raise \frac{1}{x} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

Since \frac{1^{2}}{x^{2}} and \frac{x^{3}x^{2}}{x^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 1^{2}+x^{3}x^{2}.

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

Combine like terms in 1^{2}+x^{5}.

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

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

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

Cancel out x in both numerator and denominator.

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

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

$$\frac{1+x^{5}}{x^{2}}+\frac{2xx^{2}}{x^{2}}$$

Since \frac{1+x^{5}}{x^{2}} and \frac{2xx^{2}}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{1+x^{5}+2xx^{2}}{x^{2}}$$

Do the multiplications in 1+x^{5}+2xx^{2}.

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

Factor

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