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

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

Evaluate

$$x-2$$

Short Solution Steps

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

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

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

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

Combine like terms in x-2+1.

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

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

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

Cancel out x-1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

$$x-2$$

Expand

$$x-2$$

Short Solution Steps

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

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

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

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

Combine like terms in x-2+1.

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

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

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

Cancel out x-1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

$$x-2$$