Solve n=n/x-3

$$n = \frac { n } { x } - 3$$

Solve for n

$$n=-\frac{3x}{x-1}$$

$$x\neq 1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x}{x}.

$$n=\frac{n}{x}-\frac{3x}{x}$$

Since \frac{n}{x} and \frac{3x}{x} have the same denominator, subtract them by subtracting their numerators.

$$n=\frac{n-3x}{x}$$

Subtract \frac{n-3x}{x} from both sides.

$$n-\frac{n-3x}{x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply n times \frac{x}{x}.

$$\frac{nx}{x}-\frac{n-3x}{x}=0$$

Since \frac{nx}{x} and \frac{n-3x}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{nx-\left(n-3x\right)}{x}=0$$

Do the multiplications in nx-\left(n-3x\right).

$$\frac{nx-n+3x}{x}=0$$

Multiply both sides of the equation by x.

$$nx-n+3x=0$$

Subtract 3x from both sides. Anything subtracted from zero gives its negation.

$$nx-n=-3x$$

Combine all terms containing n.

$$\left(x-1\right)n=-3x$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)n}{x-1}=-\frac{3x}{x-1}$$

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

$$n=-\frac{3x}{x-1}$$

Solve for x

$$x=\frac{n}{n+3}$$

$$n\neq 0\text{ and }n\neq -3$$

Steps for Solving Linear Equation

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

$$nx=n+x\left(-3\right)$$

Subtract x\left(-3\right) from both sides.

$$nx-x\left(-3\right)=n$$

Multiply -1 and -3 to get 3.

$$nx+3x=n$$

Combine all terms containing x.

$$\left(n+3\right)x=n$$

Divide both sides by n+3.

$$\frac{\left(n+3\right)x}{n+3}=\frac{n}{n+3}$$

Dividing by n+3 undoes the multiplication by n+3.

$$x=\frac{n}{n+3}$$

Variable x cannot be equal to 0.

$$x=\frac{n}{n+3}\text{, }x\neq 0$$