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

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

Evaluate

$$\frac{3}{x}$$

Short Solution Steps

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

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

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

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

Do the multiplications in x+1-\left(x-2\right).

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

Combine like terms in x+1-x+2.

$$\frac{3}{x-2}\times \frac{x^{2}-4x+4}{x^{2}-2x}$$

Factor the expressions that are not already factored in \frac{x^{2}-4x+4}{x^{2}-2x}.

$$\frac{3}{x-2}\times \frac{\left(x-2\right)^{2}}{x\left(x-2\right)}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{3}{x-2}\times \frac{x-2}{x}$$

Multiply \frac{3}{x-2} times \frac{x-2}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(x-2\right)}{\left(x-2\right)x}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{3}{x}$$

Expand

$$\frac{3}{x}$$

Short Solution Steps

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

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

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

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

Do the multiplications in x+1-\left(x-2\right).

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

Combine like terms in x+1-x+2.

$$\frac{3}{x-2}\times \frac{x^{2}-4x+4}{x^{2}-2x}$$

Factor the expressions that are not already factored in \frac{x^{2}-4x+4}{x^{2}-2x}.

$$\frac{3}{x-2}\times \frac{\left(x-2\right)^{2}}{x\left(x-2\right)}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{3}{x-2}\times \frac{x-2}{x}$$

Multiply \frac{3}{x-2} times \frac{x-2}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(x-2\right)}{\left(x-2\right)x}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{3}{x}$$