Solve (1/x)^2+3(1/x)+3

$$( 1 / x ) ^ { 2 } + 3 ( 1 / x ) + 3$$

Evaluate

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

Short Solution Steps

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

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

Express 3\times \frac{1}{x} as a single fraction.

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

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{3}{x} times \frac{x}{x}.

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

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

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

Combine like terms in 1^{2}+3x.

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

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

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

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

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

Factor

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