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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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