Solve 1/x-1/x-1quad(f)1/x

$$\frac { \frac { 1 } { x } - 1 } { x - 1 } \quad ( f ) \frac { 1 } { x }$$

Evaluate

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

Solution Steps

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

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

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

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

Express \frac{\frac{1-x}{x}}{x-1} as a single fraction.

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

Extract the negative sign in 1-x.

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

Cancel out x-1 in both numerator and denominator.

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

Express \frac{-1}{x}f as a single fraction.

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

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

$$\frac{-f}{xx}$$

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

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

Expand

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

Solution Steps

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

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

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

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

Express \frac{\frac{1-x}{x}}{x-1} as a single fraction.

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

Extract the negative sign in 1-x.

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

Cancel out x-1 in both numerator and denominator.

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

Express \frac{-1}{x}f as a single fraction.

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

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

$$\frac{-f}{xx}$$

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

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