Simplify (1/n-3)/(3n-1)

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

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

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

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

Combine.

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

Apply the distributive property.

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

Cancel the common factor of $n$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Simplify the denominator.

Rewrite using the commutative property of multiplication.

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

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

Move $n$ .

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

Multiply $n$ by $n$ .

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

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

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

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

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

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

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

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

Factor $n$ out of $- n$ .

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

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

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

Reduce the expression by cancelling the common factors.

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

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

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

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

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

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

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

Reorder terms.

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 1}{n}$

Move the negative in front of the fraction.

$- \frac{1}{n}$

Simplify (1/n-3)/(3n-1)

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