Solve s=1+2/2+1/3+-1-1/n

$$s = 1 + \frac { 2 } { 2 } + \frac { 1 } { 3 } + - 1 - \frac { 1 } { n }$$

Solve for n

$$n=\frac{3}{4-3s}$$

$$s\neq \frac{4}{3}$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6n, the least common multiple of 2,3,n.

$$s\times 6n=6n+3n\times 2+6n\times \frac{1}{3}+6n\left(-1\right)-6$$

Multiply 3 and 2 to get 6.

$$s\times 6n=6n+6n+6n\times \frac{1}{3}+6n\left(-1\right)-6$$

Combine 6n and 6n to get 12n.

$$s\times 6n=12n+6n\times \frac{1}{3}+6n\left(-1\right)-6$$

Multiply 6 and \frac{1}{3} to get 2.

$$s\times 6n=12n+2n+6n\left(-1\right)-6$$

Combine 12n and 2n to get 14n.

$$s\times 6n=14n+6n\left(-1\right)-6$$

Multiply 6 and -1 to get -6.

$$s\times 6n=14n-6n-6$$

Combine 14n and -6n to get 8n.

$$s\times 6n=8n-6$$

Subtract 8n from both sides.

$$s\times 6n-8n=-6$$

Combine all terms containing n.

$$\left(s\times 6-8\right)n=-6$$

The equation is in standard form.

$$\left(6s-8\right)n=-6$$

Divide both sides by 6s-8.

$$\frac{\left(6s-8\right)n}{6s-8}=-\frac{6}{6s-8}$$

Dividing by 6s-8 undoes the multiplication by 6s-8.

$$n=-\frac{6}{6s-8}$$

Divide -6 by 6s-8.

$$n=-\frac{3}{3s-4}$$

Variable n cannot be equal to 0.

$$n=-\frac{3}{3s-4}\text{, }n\neq 0$$

Solve for s

$$s=\frac{4}{3}-\frac{1}{n}$$

$$n\neq 0$$