Solve y=2x+5/x+1

$$y = \frac { 2 x + 5 } { x + 1 }$$

Solve for x

$$x=-\frac{y-5}{y-2}$$

$$y\neq 2$$

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.

$$y\left(x+1\right)=2x+5$$

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

$$yx+y=2x+5$$

Subtract 2x from both sides.

$$yx+y-2x=5$$

Subtract y from both sides.

$$yx-2x=5-y$$

Combine all terms containing x.

$$\left(y-2\right)x=5-y$$

Divide both sides by y-2.

$$\frac{\left(y-2\right)x}{y-2}=\frac{5-y}{y-2}$$

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

$$x=\frac{5-y}{y-2}$$

Variable x cannot be equal to -1.

$$x=\frac{5-y}{y-2}\text{, }x\neq -1$$

Solve for y

$$y=\frac{2x+5}{x+1}$$

$$x\neq -1$$