Solve x^3:(-x)=-x^2

$$x ^ { 3 } : ( - x ) = - x ^ { 2 }$$

Solve for x

$$x\neq 0$$

Short Solution Steps

Add x^{2} to both sides.

$$\frac{x^{3}}{-x}+x^{2}=0$$

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

$$\frac{x^{3}}{-x}+\frac{x^{2}\left(-1\right)x}{-x}=0$$

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

$$\frac{x^{3}+x^{2}\left(-1\right)x}{-x}=0$$

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

$$\frac{x^{3}-x^{3}}{-x}=0$$

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

$$\frac{0}{-x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$-0=0$$

Reorder the terms.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Variable x cannot be equal to 0.

$$x\in \mathrm{R}\setminus 0$$