Solve x^2+6x+6/x+1/x^2

$$x ^ { 2 } + 6 x + \frac { 6 } { x } + \frac { 1 } { x ^ { 2 } }$$

Evaluate

$$x^{2}+6x+\frac{6}{x}+\frac{1}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}+6x times \frac{x}{x}.

$$\frac{\left(x^{2}+6x\right)x}{x}+\frac{6}{x}+\frac{1}{x^{2}}$$

Since \frac{\left(x^{2}+6x\right)x}{x} and \frac{6}{x} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}+6x\right)x+6}{x}+\frac{1}{x^{2}}$$

Do the multiplications in \left(x^{2}+6x\right)x+6.

$$\frac{x^{3}+6x^{2}+6}{x}+\frac{1}{x^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{x^{3}+6x^{2}+6}{x} times \frac{x}{x}.

$$\frac{\left(x^{3}+6x^{2}+6\right)x}{x^{2}}+\frac{1}{x^{2}}$$

Since \frac{\left(x^{3}+6x^{2}+6\right)x}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{3}+6x^{2}+6\right)x+1}{x^{2}}$$

Do the multiplications in \left(x^{3}+6x^{2}+6\right)x+1.

$$\frac{x^{4}+6x^{3}+6x+1}{x^{2}}$$

Factor

$$\frac{x^{4}+6x^{3}+6x+1}{x^{2}}$$