Algebra Examples

$(m^{2} - 16 n^{2}) \div \frac{3 m + 12 n}{m n}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(m^{2} - 16 n^{2}) \frac{m n}{3 m + 12 n}$

Step 2

Simplify terms.

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Step 2.1

Factor $3$ out of $3 m + 12 n$ .

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Step 2.1.1

Factor $3$ out of $3 m$ .

$(m^{2} - 16 n^{2}) \frac{m n}{3 (m) + 12 n}$

Step 2.1.2

Factor $3$ out of $12 n$ .

$(m^{2} - 16 n^{2}) \frac{m n}{3 (m) + 3 (4 n)}$

Step 2.1.3

Factor $3$ out of $3 (m) + 3 (4 n)$ .

$(m^{2} - 16 n^{2}) \frac{m n}{3 (m + 4 n)}$

Step 2.2

Multiply $m^{2} - 16 n^{2}$ by $\frac{m n}{3 (m + 4 n)}$ .

$\frac{(m^{2} - 16 n^{2}) (m n)}{3 (m + 4 n)}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $16 n^{2}$ as ${(4 n)}^{2}$ .

$\frac{(m^{2} - {(4 n)}^{2}) m n}{3 (m + 4 n)}$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = 4 n$ .

$\frac{(m + 4 n) (m - (4 n)) m n}{3 (m + 4 n)}$

Step 3.3

Multiply $4$ by $- 1$ .

$\frac{(m + 4 n) (m - 4 n) m n}{3 (m + 4 n)}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $m + 4 n$ .

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Step 4.1.1

Cancel the common factor.

$\frac{(m + 4 n) (m - 4 n) m n}{3 (m + 4 n)}$

Step 4.1.2

Rewrite the expression.

$\frac{(m - 4 n) m n}{3}$

Step 4.2

Reorder factors in $\frac{(m - 4 n) m n}{3}$ .

$\frac{m n (m - 4 n)}{3}$