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

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

Solve for x

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

$$y\neq 2$$

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.

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

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

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

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

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

Subtract x from both sides.

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

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

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

Subtract y from both sides.

$$xy-2x-1=2-y$$

Add 1 to both sides.

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

Add 2 and 1 to get 3.

$$xy-2x=3-y$$

Combine all terms containing x.

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

Divide both sides by y-2.

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

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

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

Variable x cannot be equal to -1.

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

Solve for y

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

$$x\neq -1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+1.

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

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

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

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

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

Add x to both sides.

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

Combine x and x to get 2x.

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

Add 1 to both sides.

$$xy+y=2x+2+1$$

Add 2 and 1 to get 3.

$$xy+y=2x+3$$

Combine all terms containing y.

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

Divide both sides by x+1.

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

Dividing by x+1 undoes the multiplication by x+1.

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