Algebra Examples

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

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $\frac{1}{5 n}$ from both sides of the equation.

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

Step 1.2

Add $\frac{n - 1}{5 n}$ to both sides of the equation.

$\frac{1}{n} - \frac{1}{5 n} + \frac{n - 1}{5 n} = 0$

Step 2

Simplify $\frac{1}{n} - \frac{1}{5 n} + \frac{n - 1}{5 n}$ .

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Step 2.1

Combine the numerators over the common denominator.

$\frac{1}{n} + \frac{- 1 + n - 1}{5 n} = 0$

Step 2.2

Subtract $1$ from $- 1$ .

$\frac{1}{n} + \frac{n - 2}{5 n} = 0$

Step 2.3

To write $\frac{1}{n}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{n} \cdot \frac{5}{5} + \frac{n - 2}{5 n} = 0$

Step 2.4

Write each expression with a common denominator of $n \cdot 5$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{1}{n}$ by $\frac{5}{5}$ .

$\frac{5}{n \cdot 5} + \frac{n - 2}{5 n} = 0$

Step 2.4.2

Move $5$ to the left of $n$ .

$\frac{5}{5 n} + \frac{n - 2}{5 n} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{5 + n - 2}{5 n} = 0$

Step 2.6

Subtract $2$ from $5$ .

$\frac{n + 3}{5 n} = 0$

Step 3

Set the numerator equal to zero.

$n + 3 = 0$

Step 4

Subtract $3$ from both sides of the equation.

$n = - 3$