Solve x+1/x+2=a

$$\frac { x + 1 } { x + 2 } = a$$

Solve for a

$$a=\frac{x+1}{x+2}$$

$$x\neq -2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+2.

$$x+1=a\left(x+2\right)$$

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

$$x+1=ax+2a$$

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

$$ax+2a=x+1$$

Combine all terms containing a.

$$\left(x+2\right)a=x+1$$

Divide both sides by x+2.

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

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

$$a=\frac{x+1}{x+2}$$

Solve for x

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

$$a\neq 1$$

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.

$$x+1=a\left(x+2\right)$$

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

$$x+1=ax+2a$$

Subtract ax from both sides.

$$x+1-ax=2a$$

Subtract 1 from both sides.

$$x-ax=2a-1$$

Combine all terms containing x.

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

Divide both sides by 1-a.

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

Dividing by 1-a undoes the multiplication by 1-a.

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

Variable x cannot be equal to -2.

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