Solve 1-1/x^2/1+frac{1{x}}

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

Evaluate

$$\frac{x-1}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

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

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

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

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

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

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

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

Divide \frac{x^{2}-1}{x^{2}} by \frac{x+1}{x} by multiplying \frac{x^{2}-1}{x^{2}} by the reciprocal of \frac{x+1}{x}.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

$$\frac{\left(x-1\right)\left(x+1\right)}{x\left(x+1\right)}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{x-1}{x}$$

Expand

$$\frac{x-1}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

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

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

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

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

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

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

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

Divide \frac{x^{2}-1}{x^{2}} by \frac{x+1}{x} by multiplying \frac{x^{2}-1}{x^{2}} by the reciprocal of \frac{x+1}{x}.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

$$\frac{\left(x-1\right)\left(x+1\right)}{x\left(x+1\right)}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{x-1}{x}$$