Solve f(x)=x-x^2/2

$$f ( x ) = x - \frac { x ^ { 2 } } { 2 }$$

Evaluate

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

Solution Steps

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

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

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

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

Factor

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

Solution Steps

Factor out \frac{1}{2}.

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

Consider 2x-x^{2}. Factor out x.

$$x\left(2-x\right)$$

Rewrite the complete factored expression.

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