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

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

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}.

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

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

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

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

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

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

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

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

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

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

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

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

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

Calculate 1 to the power of 2 and get 1.

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

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}.

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

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

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

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

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

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

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

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

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

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

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

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

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

Calculate 1 to the power of 2 and get 1.

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