Solve xy+yx^2=2

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

Solve for y

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

$$x\neq -1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by x+x^{2}.

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

Dividing by x+x^{2} undoes the multiplication by x+x^{2}.

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

Divide 2 by x+x^{2}.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{y^{2}+8y}}{2y}-\frac{1}{2}$$

$$x=-\frac{\sqrt{y^{2}+8y}}{2y}-\frac{1}{2}\text{, }y\neq 0$$

Solve for x

$$x=\frac{\sqrt{y^{2}+8y}}{2y}-\frac{1}{2}$$

$$x=-\frac{\sqrt{y^{2}+8y}}{2y}-\frac{1}{2}\text{, }y>0\text{ or }y\leq -8$$