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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Express \frac{\frac{2x-x^{2}-1}{2-x}}{\left(x-1\right)^{2}} as a single fraction.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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

Expand the expression.

$$\frac{-x+1}{-x^{2}+3x-2}$$

Factor the expressions that are not already factored.

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

Cancel out -x+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

Express \frac{\frac{2x-x^{2}-1}{2-x}}{\left(x-1\right)^{2}} as a single fraction.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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

Expand the expression.

$$\frac{-x+1}{-x^{2}+3x-2}$$

Factor the expressions that are not already factored.

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

Cancel out -x+1 in both numerator and denominator.

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