Solve 1/x+1+2=k

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

Solve for k

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

$$x\neq -1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+1.

$$1+\left(x+1\right)\times 2=k\left(x+1\right)$$

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

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

Add 1 and 2 to get 3.

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

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

$$3+2x=kx+k$$

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

$$kx+k=3+2x$$

Combine all terms containing k.

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

The equation is in standard form.

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

Divide both sides by x+1.

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

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

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

Solve for x

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

$$k\neq 2$$

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.

$$1+\left(x+1\right)\times 2=k\left(x+1\right)$$

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

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

Add 1 and 2 to get 3.

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

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

$$3+2x=kx+k$$

Subtract kx from both sides.

$$3+2x-kx=k$$

Subtract 3 from both sides.

$$2x-kx=k-3$$

Combine all terms containing x.

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

Divide both sides by 2-k.

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

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

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

Variable x cannot be equal to -1.

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