Solve (x+1)^2-(x-y)/x^2=y

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

Solve for y (complex solution)

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

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

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

To find the opposite of x-y, find the opposite of each term.

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

Combine 2x and -x to get x.

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

Subtract yx^{2} from both sides.

$$x^{2}+x+1+y-yx^{2}=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Subtract x from both sides.

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

Subtract 1 from both sides.

$$y-yx^{2}=-x^{2}-x-1$$

Combine all terms containing y.

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

Divide both sides by 1-x^{2}.

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

Dividing by 1-x^{2} undoes the multiplication by 1-x^{2}.

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

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

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

Solve for y

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

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

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

To find the opposite of x-y, find the opposite of each term.

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

Combine 2x and -x to get x.

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

Subtract yx^{2} from both sides.

$$x^{2}+x+1+y-yx^{2}=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Subtract x from both sides.

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

Subtract 1 from both sides.

$$y-yx^{2}=-x^{2}-x-1$$

Combine all terms containing y.

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

Divide both sides by 1-x^{2}.

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

Dividing by 1-x^{2} undoes the multiplication by 1-x^{2}.

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

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

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{4y^{2}-3}+1}{2\left(1-y\right)}\text{, }&y\neq 1\\x=\frac{\sqrt{4y^{2}-3}-1}{2\left(1-y\right)}\text{, }&y\neq 1\text{ and }y\neq -1\\x=-2\text{, }&y=1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{4y^{2}-3}+1}{2\left(1-y\right)}\text{, }&\left(y\neq 1\text{ and }y\geq \frac{\sqrt{3}}{2}\right)\text{ or }y\leq -\frac{\sqrt{3}}{2}\\x=\frac{\sqrt{4y^{2}-3}-1}{2\left(1-y\right)}\text{, }&\left(y\neq 1\text{ and }y\geq \frac{\sqrt{3}}{2}\right)\text{ or }\left(y\neq -1\text{ and }y\leq -\frac{\sqrt{3}}{2}\right)\\x=-2\text{, }&y=1\end{matrix}\right.$$