Solve 1-x^2/2x+1

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

Evaluate

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

Short Solution Steps

Express \frac{x^{2}}{2}x as a single fraction.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

Since \frac{2}{2} and \frac{x^{3}}{2} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Since \frac{2-x^{3}}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

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

Combine like terms in 2-x^{3}+2.

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

Factor

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

Solution Steps

Factor out \frac{1}{2}. Polynomial -x^{3}+4 is not factored since it does not have any rational roots.

$$\frac{4-x^{2}x}{2}$$