Solve (1-1/x)(1+1/x)

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Multiply \frac{x-1}{x} times \frac{x+1}{x} by multiplying numerator times numerator and denominator times denominator.

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

Multiply x and x to get x^{2}.

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

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 1 to the power of 2 and get 1.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

Multiply \frac{x-1}{x} times \frac{x+1}{x} by multiplying numerator times numerator and denominator times denominator.

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

Multiply x and x to get x^{2}.

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

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 1 to the power of 2 and get 1.

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