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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Multiply \frac{x^{2}+1-2x}{2} times \frac{1}{x-1} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

Multiply \frac{x^{2}+1-2x}{2} times \frac{1}{x-1} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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