Solve yx^2+x-y+1=0

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

Solve for y (complex solution)

$$\left\{\begin{matrix}y=-\frac{1}{x-1}\text{, }&x\neq 1\\y\in \mathrm{C}\text{, }&x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x from both sides. Anything subtracted from zero gives its negation.

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

Subtract 1 from both sides.

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

Combine all terms containing y.

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

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

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

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

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

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

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

Solve for y

$$\left\{\begin{matrix}y=-\frac{1}{x-1}\text{, }&x\neq 1\\y\in \mathrm{R}\text{, }&x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x from both sides. Anything subtracted from zero gives its negation.

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

Subtract 1 from both sides.

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

Combine all terms containing y.

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

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

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

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

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

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

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

Solve for x

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