Solve -2x^3+xdivx^2+1

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

Evaluate

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

Short Solution Steps

Rewrite x^{2} as xx. Cancel out x in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -2x^{3}+1 times \frac{x}{x}.

$$\frac{\left(-2x^{3}+1\right)x}{x}+\frac{1}{x}$$

Since \frac{\left(-2x^{3}+1\right)x}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\frac{\left(-2x^{3}+1\right)x+1}{x}$$

Do the multiplications in \left(-2x^{3}+1\right)x+1.

$$\frac{-2x^{4}+x+1}{x}$$

Factor

$$-\frac{\left(x-1\right)\left(2x^{3}+2x^{2}+2x+1\right)}{x}$$