Solve y=2-3/x+1

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

Solve for x

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

$$y\neq 2$$

Steps for Solving Linear Equation

Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by x+1.

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

Use the distributive property to multiply y by x+1.

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

Use the distributive property to multiply x+1 by 2.

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

Subtract 3 from 2 to get -1.

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

Subtract 2x from both sides.

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

Subtract y from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y-2.

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

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

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

Divide -1-y by y-2.

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

Variable x cannot be equal to -1.

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

Solve for y

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

$$x\neq -1$$