Algebra Examples

$\frac{(\frac{1}{n} - 3)}{3 n - 1}$

Step 1

Multiply the numerator and denominator of the fraction by $n$ .

Tap for more steps...

Step 1.1

Multiply $\frac{\frac{1}{n} - 3}{3 n - 1}$ by $\frac{n}{n}$ .

$\frac{n}{n} \cdot \frac{\frac{1}{n} - 3}{3 n - 1}$

Step 1.2

Combine.

$\frac{n (\frac{1}{n} - 3)}{n (3 n - 1)}$

Step 2

Apply the distributive property.

$\frac{n \frac{1}{n} + n \cdot - 3}{n (3 n) + n \cdot - 1}$

Step 3

Cancel the common factor of $n$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{n \frac{1}{n} + n \cdot - 3}{n (3 n) + n \cdot - 1}$

Step 3.2

Rewrite the expression.

$\frac{1 + n \cdot - 3}{n (3 n) + n \cdot - 1}$

Step 4

Move $- 3$ to the left of $n$ .

$\frac{1 - 3 n}{n (3 n) + n \cdot - 1}$

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

Rewrite using the commutative property of multiplication.

$\frac{1 - 3 n}{3 n \cdot n + n \cdot - 1}$

Step 5.2

Multiply $n$ by $n$ by adding the exponents.

Tap for more steps...

Step 5.2.1

Move $n$ .

$\frac{1 - 3 n}{3 (n \cdot n) + n \cdot - 1}$

Step 5.2.2

Multiply $n$ by $n$ .

$\frac{1 - 3 n}{3 n^{2} + n \cdot - 1}$

Step 5.3

Move $- 1$ to the left of $n$ .

$\frac{1 - 3 n}{3 n^{2} - 1 \cdot n}$

Step 5.4

Rewrite $- 1 n$ as $- n$ .

$\frac{1 - 3 n}{3 n^{2} - n}$

Step 5.5

Factor $n$ out of $3 n^{2} - n$ .

Tap for more steps...

Step 5.5.1

Factor $n$ out of $3 n^{2}$ .

$\frac{1 - 3 n}{n (3 n) - n}$

Step 5.5.2

Factor $n$ out of $- n$ .

$\frac{1 - 3 n}{n (3 n) + n \cdot - 1}$

Step 5.5.3

Factor $n$ out of $n (3 n) + n \cdot - 1$ .

$\frac{1 - 3 n}{n (3 n - 1)}$

Step 6

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 6.1

Cancel the common factor of $1 - 3 n$ and $3 n - 1$ .

Tap for more steps...

Step 6.1.1

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- 1 (- 1) - 3 n}{n (3 n - 1)}$

Step 6.1.2

Factor $- 1$ out of $- 3 n$ .

$\frac{- 1 (- 1) - (3 n)}{n (3 n - 1)}$

Step 6.1.3

Factor $- 1$ out of $- 1 (- 1) - (3 n)$ .

$\frac{- 1 (- 1 + 3 n)}{n (3 n - 1)}$

Step 6.1.4

Reorder terms.

$\frac{- 1 (3 n - 1)}{n (3 n - 1)}$

Step 6.1.5

Cancel the common factor.

$\frac{- 1 (3 n - 1)}{n (3 n - 1)}$

Step 6.1.6

Rewrite the expression.

$\frac{- 1}{n}$

Step 6.2

Move the negative in front of the fraction.

$- \frac{1}{n}$