Divide ((n-4)/(7n^2-28n))÷((3n)/(n-2))

$\frac{n - 4}{7 n^{2} - 28 n} \div \frac{3 n}{n - 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{n - 4}{7 n^{2} - 28 n} \cdot \frac{n - 2}{3 n}$

Step 2

Factor $7 n$ out of $7 n^{2} - 28 n$ .

Factor $7 n$ out of $7 n^{2}$ .

$\frac{n - 4}{7 n (n) - 28 n} \cdot \frac{n - 2}{3 n}$

Factor $7 n$ out of $- 28 n$ .

$\frac{n - 4}{7 n (n) + 7 n (- 4)} \cdot \frac{n - 2}{3 n}$

Factor $7 n$ out of $7 n (n) + 7 n (- 4)$ .

$\frac{n - 4}{7 n (n - 4)} \cdot \frac{n - 2}{3 n}$

Step 3

Cancel the common factor of $n - 4$ .

Cancel the common factor.

$\frac{n - 4}{7 n (n - 4)} \cdot \frac{n - 2}{3 n}$

Rewrite the expression.

$\frac{1}{7 n} \cdot \frac{n - 2}{3 n}$

Step 4

Multiply $\frac{1}{7 n} \cdot \frac{n - 2}{3 n}$ .

Multiply $\frac{1}{7 n}$ by $\frac{n - 2}{3 n}$ .

$\frac{n - 2}{7 n (3 n)}$

Multiply $3$ by $7$ .

$\frac{n - 2}{21 n \cdot n}$

Raise $n$ to the power of $1$ .

$\frac{n - 2}{21 (n^{1} n)}$

Raise $n$ to the power of $1$ .

$\frac{n - 2}{21 (n^{1} n^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{n - 2}{21 n^{1 + 1}}$

Add $1$ and $1$ .

$\frac{n - 2}{21 n^{2}}$

Step 5

Split the fraction $\frac{n - 2}{21 n^{2}}$ into two fractions.

$\frac{n}{21 n^{2}} + \frac{- 2}{21 n^{2}}$

Step 6

Cancel the common factor of $n$ and $n^{2}$ .

Raise $n$ to the power of $1$ .

$\frac{n^{1}}{21 n^{2}} + \frac{- 2}{21 n^{2}}$

Factor $n$ out of $n^{1}$ .

$\frac{n \cdot 1}{21 n^{2}} + \frac{- 2}{21 n^{2}}$

Cancel the common factors.

Factor $n$ out of $21 n^{2}$ .

$\frac{n \cdot 1}{n (21 n)} + \frac{- 2}{21 n^{2}}$

Cancel the common factor.

$\frac{n \cdot 1}{n (21 n)} + \frac{- 2}{21 n^{2}}$

Rewrite the expression.

$\frac{1}{21 n} + \frac{- 2}{21 n^{2}}$

Step 7

Move the negative in front of the fraction.

$\frac{1}{21 n} - \frac{2}{21 n^{2}}$

Divide ((n-4)/(7n^2-28n))÷((3n)/(n-2))

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