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

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

Solve for y

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

$$x\neq -3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+3.

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

Use the distributive property to multiply x+3 by y.

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

To find the opposite of xy+3y, find the opposite of each term.

$$-xy-3y=x^{2}-x-2$$

Combine all terms containing y.

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

Divide both sides by -x-3.

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

Dividing by -x-3 undoes the multiplication by -x-3.

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

Divide \left(-2+x\right)\left(1+x\right) by -x-3.

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

Solve for x (complex solution)

$$x=\frac{-\sqrt{y^{2}-14y+9}-y+1}{2}$$

$$x=\frac{\sqrt{y^{2}-14y+9}-y+1}{2}$$

Solve for x

$$x=\frac{-\sqrt{y^{2}-14y+9}-y+1}{2}$$

$$x=\frac{\sqrt{y^{2}-14y+9}-y+1}{2}\text{, }y\geq 2\sqrt{10}+7\text{ or }y\leq 7-2\sqrt{10}$$