Basic Math Examples

$(\frac{5 n + 15}{4 n + 8}) (\frac{2 n + 4}{3 n + 9})$

Step 1

Factor $5$ out of $5 n + 15$ .

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Step 1.1

Factor $5$ out of $5 n$ .

$\frac{5 (n) + 15}{4 n + 8} \cdot \frac{2 n + 4}{3 n + 9}$

Step 1.2

Factor $5$ out of $15$ .

$\frac{5 n + 5 \cdot 3}{4 n + 8} \cdot \frac{2 n + 4}{3 n + 9}$

Step 1.3

Factor $5$ out of $5 n + 5 \cdot 3$ .

$\frac{5 (n + 3)}{4 n + 8} \cdot \frac{2 n + 4}{3 n + 9}$

Step 2

Factor $4$ out of $4 n + 8$ .

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Step 2.1

Factor $4$ out of $4 n$ .

$\frac{5 (n + 3)}{4 (n) + 8} \cdot \frac{2 n + 4}{3 n + 9}$

Step 2.2

Factor $4$ out of $8$ .

$\frac{5 (n + 3)}{4 n + 4 \cdot 2} \cdot \frac{2 n + 4}{3 n + 9}$

Step 2.3

Factor $4$ out of $4 n + 4 \cdot 2$ .

$\frac{5 (n + 3)}{4 (n + 2)} \cdot \frac{2 n + 4}{3 n + 9}$

Step 3

Factor $2$ out of $2 n + 4$ .

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Step 3.1

Factor $2$ out of $2 n$ .

$\frac{5 (n + 3)}{4 (n + 2)} \cdot \frac{2 (n) + 4}{3 n + 9}$

Step 3.2

Factor $2$ out of $4$ .

$\frac{5 (n + 3)}{4 (n + 2)} \cdot \frac{2 n + 2 \cdot 2}{3 n + 9}$

Step 3.3

Factor $2$ out of $2 n + 2 \cdot 2$ .

$\frac{5 (n + 3)}{4 (n + 2)} \cdot \frac{2 (n + 2)}{3 n + 9}$

Step 4

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

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Step 4.1

Factor $3$ out of $3 n$ .

$\frac{5 (n + 3)}{4 (n + 2)} \cdot \frac{2 (n + 2)}{3 (n) + 9}$

Step 4.2

Factor $3$ out of $9$ .

$\frac{5 (n + 3)}{4 (n + 2)} \cdot \frac{2 (n + 2)}{3 n + 3 \cdot 3}$

Step 4.3

Factor $3$ out of $3 n + 3 \cdot 3$ .

$\frac{5 (n + 3)}{4 (n + 2)} \cdot \frac{2 (n + 2)}{3 (n + 3)}$

Step 5

Cancel the common factor of $n + 3$ .

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Step 5.1

Factor $n + 3$ out of $5 (n + 3)$ .

$\frac{(n + 3) \cdot 5}{4 (n + 2)} \cdot \frac{2 (n + 2)}{3 (n + 3)}$

Step 5.2

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

$\frac{(n + 3) \cdot 5}{4 (n + 2)} \cdot \frac{2 (n + 2)}{(n + 3) \cdot 3}$

Step 5.3

Cancel the common factor.

$\frac{(n + 3) \cdot 5}{4 (n + 2)} \cdot \frac{2 (n + 2)}{(n + 3) \cdot 3}$

Step 5.4

Rewrite the expression.

$\frac{5}{4 (n + 2)} \cdot \frac{2 (n + 2)}{3}$

Step 6

Cancel the common factor of $2 (n + 2)$ .

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Step 6.1

Factor $2 (n + 2)$ out of $4 (n + 2)$ .

$\frac{5}{2 (n + 2) (2)} \cdot \frac{2 (n + 2)}{3}$

Step 6.2

Cancel the common factor.

$\frac{5}{2 (n + 2) \cdot 2} \cdot \frac{2 (n + 2)}{3}$

Step 6.3

Rewrite the expression.

$\frac{5}{2} \cdot \frac{1}{3}$

Step 7

Multiply $\frac{5}{2}$ by $\frac{1}{3}$ .

$\frac{5}{2 \cdot 3}$

Step 8

Multiply $2$ by $3$ .

$\frac{5}{6}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{6}$

Decimal Form:

$0.8\overline{3}$