Solve x-2/x^2-1div(1-1/x-1)

$$\frac { x - 2 } { x ^ { 2 } - 1 } \div ( 1 - \frac { 1 } { x - 1 } )$$

Evaluate

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

Short Solution Steps

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

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

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

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

Combine like terms in x-1-1.

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

Divide \frac{x-2}{x^{2}-1} by \frac{x-2}{x-1} by multiplying \frac{x-2}{x^{2}-1} by the reciprocal of \frac{x-2}{x-1}.

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

Cancel out x-2 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

Combine like terms in x-1-1.

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

Divide \frac{x-2}{x^{2}-1} by \frac{x-2}{x-1} by multiplying \frac{x-2}{x^{2}-1} by the reciprocal of \frac{x-2}{x-1}.

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

Cancel out x-2 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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