Basic Math Examples

$\frac{3 n^{2} + 9 n}{2 n} \div \frac{n + 3}{4}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 n^{2} + 9 n}{2 n} \cdot \frac{4}{n + 3}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $2$ .

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Step 2.1.1

Factor $2$ out of $2 n$ .

$\frac{3 n^{2} + 9 n}{2 (n)} \cdot \frac{4}{n + 3}$

Step 2.1.2

Factor $2$ out of $4$ .

$\frac{3 n^{2} + 9 n}{2 (n)} \cdot \frac{2 (2)}{n + 3}$

Step 2.1.3

Cancel the common factor.

$\frac{3 n^{2} + 9 n}{2 n} \cdot \frac{2 \cdot 2}{n + 3}$

Step 2.1.4

Rewrite the expression.

$\frac{3 n^{2} + 9 n}{n} \cdot \frac{2}{n + 3}$

Step 2.2

Multiply $\frac{3 n^{2} + 9 n}{n}$ by $\frac{2}{n + 3}$ .

$\frac{(3 n^{2} + 9 n) \cdot 2}{n (n + 3)}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $3 n$ out of $3 n^{2} + 9 n$ .

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Step 3.1.1

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

$\frac{(3 n (n) + 9 n) \cdot 2}{n (n + 3)}$

Step 3.1.2

Factor $3 n$ out of $9 n$ .

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

Step 3.1.3

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

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

Step 3.2

Multiply $2$ by $3$ .

$\frac{6 n (n + 3)}{n (n + 3)}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $n$ .

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Step 4.1.1

Cancel the common factor.

$\frac{6 n (n + 3)}{n (n + 3)}$

Step 4.1.2

Rewrite the expression.

$\frac{6 (n + 3)}{n + 3}$

Step 4.2

Cancel the common factor of $n + 3$ .

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Step 4.2.1

Cancel the common factor.

$\frac{6 (n + 3)}{n + 3}$

Step 4.2.2

Divide $6$ by $1$ .

$6$