Simplify x-(x^3)/(x^2+y)

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

To write $x$ as a fraction with a common denominator, multiply by $\frac{x^{2} + y}{x^{2} + y}$ .

$\frac{x (x^{2} + y)}{x^{2} + y} - \frac{x^{3}}{x^{2} + y}$

Combine the numerators over the common denominator.

$\frac{x (x^{2} + y) - x^{3}}{x^{2} + y}$

Simplify the numerator.

Factor $x$ out of $x (x^{2} + y) - x^{3}$ .

Factor $x$ out of $- x^{3}$ .

$\frac{x (x^{2} + y) + x (- x^{2})}{x^{2} + y}$

Factor $x$ out of $x (x^{2} + y) + x (- x^{2})$ .

$\frac{x (x^{2} + y - x^{2})}{x^{2} + y}$

Subtract $x^{2}$ from $x^{2}$ .

$\frac{x (y + 0)}{x^{2} + y}$

Add $y$ and $0$ .

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