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

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

Evaluate

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

Short Solution Steps

Use the distributive property to multiply x by x-1.

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

To find the opposite of x-1, find the opposite of each term.

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

The opposite of -1 is 1.

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

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

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

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

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

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

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

Combine like terms in x^{2}-x-2x+2.

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

Expand

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

Short Solution Steps

Use the distributive property to multiply x by x-1.

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

To find the opposite of x-1, find the opposite of each term.

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

The opposite of -1 is 1.

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

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

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

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

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

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

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

Combine like terms in x^{2}-x-2x+2.

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