Solve y=x-3x-1/x-2

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

Solve for x

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

$$y\neq -2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.

$$y\left(x-2\right)=x-3x-1$$

Use the distributive property to multiply y by x-2.

$$yx-2y=x-3x-1$$

Combine x and -3x to get -2x.

$$yx-2y=-2x-1$$

Add 2x to both sides.

$$yx-2y+2x=-1$$

Add 2y to both sides.

$$yx+2x=-1+2y$$

Combine all terms containing x.

$$\left(y+2\right)x=-1+2y$$

The equation is in standard form.

$$\left(y+2\right)x=2y-1$$

Divide both sides by y+2.

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

Dividing by y+2 undoes the multiplication by y+2.

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

Variable x cannot be equal to 2.

$$x=\frac{2y-1}{y+2}\text{, }x\neq 2$$

Solve for y

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

$$x\neq 2$$