Solve f(x)=2x-3/x+1=y

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

Solve for x

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

$$y\neq 2$$

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.

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

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

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

Subtract yx from both sides.

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

Add 3 to both sides.

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

Combine all terms containing x.

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

Divide both sides by -y+2.

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

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

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

Variable x cannot be equal to -1.

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

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.

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

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

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

Swap sides so that all variable terms are on the left hand side.

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

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.

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