Solve =(1/x)^2+2x1/xxx+x^2

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

Evaluate

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

Short Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

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

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

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

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

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

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

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

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

Combine like terms in 1^{2}+x^{4}.

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

Express \frac{2}{x}x^{3} as a single fraction.

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

Cancel out x in both numerator and denominator.

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

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

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

Since \frac{1+x^{4}}{x^{2}} and \frac{2x^{2}x^{2}}{x^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 1+x^{4}+2x^{2}x^{2}.

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

Combine like terms in 1+x^{4}+2x^{4}.

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

Factor

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