Solve 1+1/x+1/x^2+1/x^3+1/x^4

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

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

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

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

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+1}{x} times \frac{x}{x}.

$$\frac{\left(x+1\right)x}{x^{2}}+\frac{1}{x^{2}}+\frac{1}{x^{3}}+\frac{1}{x^{4}}$$

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

$$\frac{\left(x+1\right)x+1}{x^{2}}+\frac{1}{x^{3}}+\frac{1}{x^{4}}$$

Do the multiplications in \left(x+1\right)x+1.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and x^{3} is x^{3}. Multiply \frac{x^{2}+x+1}{x^{2}} times \frac{x}{x}.

$$\frac{\left(x^{2}+x+1\right)x}{x^{3}}+\frac{1}{x^{3}}+\frac{1}{x^{4}}$$

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

$$\frac{\left(x^{2}+x+1\right)x+1}{x^{3}}+\frac{1}{x^{4}}$$

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{3} and x^{4} is x^{4}. Multiply \frac{x^{3}+x^{2}+x+1}{x^{3}} times \frac{x}{x}.

$$\frac{\left(x^{3}+x^{2}+x+1\right)x}{x^{4}}+\frac{1}{x^{4}}$$

Since \frac{\left(x^{3}+x^{2}+x+1\right)x}{x^{4}} and \frac{1}{x^{4}} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{3}+x^{2}+x+1\right)x+1}{x^{4}}$$

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

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

Factor

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