Solve 1/x-1/frac{1{x}+3}

$$\frac { \frac { 1 } { x } - 1 } { \frac { 1 } { x } + 3 }$$

Evaluate

$$\frac{1-x}{3x+1}$$

Solution Steps

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

$$\frac{\frac{1}{x}-\frac{x}{x}}{\frac{1}{x}+3}$$

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

$$\frac{\frac{1-x}{x}}{\frac{1}{x}+3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x}{x}.

$$\frac{\frac{1-x}{x}}{\frac{1}{x}+\frac{3x}{x}}$$

Since \frac{1}{x} and \frac{3x}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1-x}{x}}{\frac{1+3x}{x}}$$

Divide \frac{1-x}{x} by \frac{1+3x}{x} by multiplying \frac{1-x}{x} by the reciprocal of \frac{1+3x}{x}.

$$\frac{\left(1-x\right)x}{x\left(1+3x\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{-x+1}{3x+1}$$

Expand

$$\frac{1-x}{3x+1}$$

Solution Steps

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

$$\frac{\frac{1}{x}-\frac{x}{x}}{\frac{1}{x}+3}$$

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

$$\frac{\frac{1-x}{x}}{\frac{1}{x}+3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x}{x}.

$$\frac{\frac{1-x}{x}}{\frac{1}{x}+\frac{3x}{x}}$$

Since \frac{1}{x} and \frac{3x}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1-x}{x}}{\frac{1+3x}{x}}$$

Divide \frac{1-x}{x} by \frac{1+3x}{x} by multiplying \frac{1-x}{x} by the reciprocal of \frac{1+3x}{x}.

$$\frac{\left(1-x\right)x}{x\left(1+3x\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{-x+1}{3x+1}$$