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, add them by adding 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

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

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, add them by adding 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.

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