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x-\frac{x^{3}}{x^{2}+4}=0
Subtract \frac{x^{3}}{x^{2}+4} from both sides.
\frac{x\left(x^{2}+4\right)}{x^{2}+4}-\frac{x^{3}}{x^{2}+4}=0
To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x^{2}+4}{x^{2}+4}.
\frac{x\left(x^{2}+4\right)-x^{3}}{x^{2}+4}=0
Since \frac{x\left(x^{2}+4\right)}{x^{2}+4} and \frac{x^{3}}{x^{2}+4} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{3}+4x-x^{3}}{x^{2}+4}=0
Do the multiplications in x\left(x^{2}+4\right)-x^{3}.
\frac{4x}{x^{2}+4}=0
Combine like terms in x^{3}+4x-x^{3}.
4x=0
Multiply both sides of the equation by x^{2}+4.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since 4 is not equal to 0, x must be equal to 0.