Solve A_{N}=5N/N+3

$$A _ { N } = \frac { 5 N } { N + 3 }$$

Solve for N

$$N=\frac{3A_{N}}{5-A_{N}}$$

$$A_{N}\neq 5$$

Steps for Solving Linear Equation

Variable N cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by N+3.

$$A_{N}\left(N+3\right)=5N$$

Use the distributive property to multiply A_{N} by N+3.

$$A_{N}N+3A_{N}=5N$$

Subtract 5N from both sides.

$$A_{N}N+3A_{N}-5N=0$$

Subtract 3A_{N} from both sides. Anything subtracted from zero gives its negation.

$$A_{N}N-5N=-3A_{N}$$

Combine all terms containing N.

$$\left(A_{N}-5\right)N=-3A_{N}$$

Divide both sides by A_{N}-5.

$$\frac{\left(A_{N}-5\right)N}{A_{N}-5}=-\frac{3A_{N}}{A_{N}-5}$$

Dividing by A_{N}-5 undoes the multiplication by A_{N}-5.

$$N=-\frac{3A_{N}}{A_{N}-5}$$

Variable N cannot be equal to -3.

$$N=-\frac{3A_{N}}{A_{N}-5}\text{, }N\neq -3$$

Solve for A_N

$$A_{N}=\frac{5N}{N+3}$$

$$N\neq -3$$