Basic Math Examples

$\frac{9 c + 45}{6 c^{12}} \cdot \frac{c^{5}}{c^{2} - 25}$

Step 1

Factor $9$ out of $9 c + 45$ .

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Step 1.1

Factor $9$ out of $9 c$ .

$\frac{9 (c) + 45}{6 c^{12}} \cdot \frac{c^{5}}{c^{2} - 25}$

Step 1.2

Factor $9$ out of $45$ .

$\frac{9 c + 9 \cdot 5}{6 c^{12}} \cdot \frac{c^{5}}{c^{2} - 25}$

Step 1.3

Factor $9$ out of $9 c + 9 \cdot 5$ .

$\frac{9 (c + 5)}{6 c^{12}} \cdot \frac{c^{5}}{c^{2} - 25}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $25$ as $5^{2}$ .

$\frac{9 (c + 5)}{6 c^{12}} \cdot \frac{c^{5}}{c^{2} - 5^{2}}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = c$ and $b = 5$ .

$\frac{9 (c + 5)}{6 c^{12}} \cdot \frac{c^{5}}{(c + 5) (c - 5)}$

Step 3

Simplify terms.

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Step 3.1

Combine.

$\frac{9 (c + 5) c^{5}}{6 c^{12} ((c + 5) (c - 5))}$

Step 3.2

Cancel the common factor of $9$ and $6$ .

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Step 3.2.1

Factor $3$ out of $9 (c + 5) c^{5}$ .

$\frac{3 (3 (c + 5) c^{5})}{6 c^{12} ((c + 5) (c - 5))}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $3$ out of $6 c^{12} ((c + 5) (c - 5))$ .

$\frac{3 (3 (c + 5) c^{5})}{3 (2 c^{12} ((c + 5) (c - 5)))}$

Step 3.2.2.2

Cancel the common factor.

$\frac{3 (3 (c + 5) c^{5})}{3 (2 c^{12} ((c + 5) (c - 5)))}$

Step 3.2.2.3

Rewrite the expression.

$\frac{3 (c + 5) c^{5}}{2 c^{12} ((c + 5) (c - 5))}$

Step 3.3

Cancel the common factor of $c + 5$ .

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Step 3.3.1

Cancel the common factor.

$\frac{3 (c + 5) c^{5}}{2 c^{12} ((c + 5) (c - 5))}$

Step 3.3.2

Rewrite the expression.

$\frac{3 c^{5}}{2 c^{12} (c - 5)}$

Step 3.4

Cancel the common factor of $c^{5}$ and $c^{12}$ .

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Step 3.4.1

Factor $c^{5}$ out of $3 c^{5}$ .

$\frac{c^{5} \cdot 3}{2 c^{12} (c - 5)}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $c^{5}$ out of $2 c^{12} (c - 5)$ .

$\frac{c^{5} \cdot 3}{c^{5} (2 c^{7} (c - 5))}$

Step 3.4.2.2

Cancel the common factor.

$\frac{c^{5} \cdot 3}{c^{5} (2 c^{7} (c - 5))}$

Step 3.4.2.3

Rewrite the expression.

$\frac{3}{2 c^{7} (c - 5)}$