Solve 1/n=1/5n-n-1/5n

$$\frac { 1 } { n } = \frac { 1 } { 5 n } - \frac { n - 1 } { 5 n }$$

Solve for n

$$n=-3$$

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 5n, the least common multiple of n,5n.

$$5=1-\left(n-1\right)$$

To find the opposite of n-1, find the opposite of each term.

$$5=1-n+1$$

Add 1 and 1 to get 2.

$$5=2-n$$

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

$$2-n=5$$

Subtract 2 from both sides.

$$-n=5-2$$

Subtract 2 from 5 to get 3.

$$-n=3$$

Multiply both sides by -1.

$$n=-3$$