Solve a-r/a=n/1

$$\frac { a - r } { a } = \frac { n } { 1 }$$

Solve for a

$$\left\{\begin{matrix}a=\frac{r}{1-n}\text{, }&r\neq 0\text{ and }n\neq 1\\a\neq 0\text{, }&r=0\text{ and }n=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$a-r=an$$

Subtract an from both sides.

$$a-r-an=0$$

Add r to both sides. Anything plus zero gives itself.

$$a-an=r$$

Combine all terms containing a.

$$\left(1-n\right)a=r$$

Divide both sides by 1-n.

$$\frac{\left(1-n\right)a}{1-n}=\frac{r}{1-n}$$

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

$$a=\frac{r}{1-n}$$

Variable a cannot be equal to 0.

$$a=\frac{r}{1-n}\text{, }a\neq 0$$

Solve for n

$$n=\frac{a-r}{a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$a-r=an$$

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

$$an=a-r$$

Divide both sides by a.

$$\frac{an}{a}=\frac{a-r}{a}$$

Dividing by a undoes the multiplication by a.

$$n=\frac{a-r}{a}$$