Solve x^3+yx^2+x^2+yx=1

$${ x }^{ 3 } +y { x }^{ 2 } + { x }^{ 2 } +yx=1$$

Solve for y

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

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

Steps for Solving Linear Equation

Subtract x^{3} from both sides.

$$yx^{2}+x^{2}+yx=1-x^{3}$$

Subtract x^{2} from both sides.

$$yx^{2}+yx=1-x^{3}-x^{2}$$

Combine all terms containing y.

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

The equation is in standard form.

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

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

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

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

$$y=\frac{1-x^{2}-x^{3}}{x^{2}+x}$$

Divide -x^{3}-x^{2}+1 by x^{2}+x.

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