Solve frac{n_{t}}{n-1}=5/3

$$\frac { n _ { t } } { n - 1 } = \frac { 5 } { 3 }$$

Solve for n

$$n=\frac{3n_{t}}{5}+1$$

$$n_{t}\neq 0$$

Steps for Solving Linear Equation

Variable n cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 3\left(n-1\right), the least common multiple of n-1,3.

$$3n_{t}=5\left(n-1\right)$$

Use the distributive property to multiply 5 by n-1.

$$3n_{t}=5n-5$$

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

$$5n-5=3n_{t}$$

Add 5 to both sides.

$$5n=3n_{t}+5$$

Divide both sides by 5.

$$\frac{5n}{5}=\frac{3n_{t}+5}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$n=\frac{3n_{t}+5}{5}$$

Divide 3n_{t}+5 by 5.

$$n=\frac{3n_{t}}{5}+1$$

Variable n cannot be equal to 1.

$$n=\frac{3n_{t}}{5}+1\text{, }n\neq 1$$

Solve for n_t

$$n_{t}=\frac{5\left(n-1\right)}{3}$$

$$n\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3\left(n-1\right), the least common multiple of n-1,3.

$$3n_{t}=5\left(n-1\right)$$

Use the distributive property to multiply 5 by n-1.

$$3n_{t}=5n-5$$

Divide both sides by 3.

$$\frac{3n_{t}}{3}=\frac{5n-5}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$n_{t}=\frac{5n-5}{3}$$