Solve y=x^2+x^3/x

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

Solve for y

$$y=x\left(x+1\right)$$

$$x\neq 0$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+x^{3}}{x}.

$$y=\frac{\left(x+1\right)x^{2}}{x}$$

Cancel out x in both numerator and denominator.

$$y=x\left(x+1\right)$$

Expand the expression.

$$y=x^{2}+x$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{-\sqrt{4y+1}-1}{2}\text{, }&\text{unconditionally}\\x=\frac{\sqrt{4y+1}-1}{2}\text{, }&y\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{4y+1}-1}{2}\text{, }&y\neq 0\text{ and }y\geq -\frac{1}{4}\\x=\frac{-\sqrt{4y+1}-1}{2}\text{, }&y\geq -\frac{1}{4}\end{matrix}\right.$$