Solve (1+1/x-2)divx^2-2x+1/x^2-4

$$( 1 + \frac { 1 } { x - 2 } ) \div \frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 4 }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-2}{x-2}.

$$\frac{\frac{x-2}{x-2}+\frac{1}{x-2}}{\frac{x^{2}-2x+1}{x^{2}-4}}$$

Since \frac{x-2}{x-2} and \frac{1}{x-2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x-2+1}{x-2}}{\frac{x^{2}-2x+1}{x^{2}-4}}$$

Combine like terms in x-2+1.

$$\frac{\frac{x-1}{x-2}}{\frac{x^{2}-2x+1}{x^{2}-4}}$$

Divide \frac{x-1}{x-2} by \frac{x^{2}-2x+1}{x^{2}-4} by multiplying \frac{x-1}{x-2} by the reciprocal of \frac{x^{2}-2x+1}{x^{2}-4}.

$$\frac{\left(x-1\right)\left(x^{2}-4\right)}{\left(x-2\right)\left(x^{2}-2x+1\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-2\right)\left(x-1\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-2}{x-2}.

$$\frac{\frac{x-2}{x-2}+\frac{1}{x-2}}{\frac{x^{2}-2x+1}{x^{2}-4}}$$

Since \frac{x-2}{x-2} and \frac{1}{x-2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x-2+1}{x-2}}{\frac{x^{2}-2x+1}{x^{2}-4}}$$

Combine like terms in x-2+1.

$$\frac{\frac{x-1}{x-2}}{\frac{x^{2}-2x+1}{x^{2}-4}}$$

Divide \frac{x-1}{x-2} by \frac{x^{2}-2x+1}{x^{2}-4} by multiplying \frac{x-1}{x-2} by the reciprocal of \frac{x^{2}-2x+1}{x^{2}-4}.

$$\frac{\left(x-1\right)\left(x^{2}-4\right)}{\left(x-2\right)\left(x^{2}-2x+1\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-2\right)\left(x-1\right) in both numerator and denominator.

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