Solve f(x+1/x)=x^2+1/x^2+1/x

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

Evaluate

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

Short Solution Steps

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

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

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

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

Expand

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

Short Solution Steps

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

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

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

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