Basic Math Examples

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

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $4$ as $2^{2}$ .

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

Step 1.2

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 $b = 2$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $9$ as $3^{2}$ .

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

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 $b = 3$ .

$\frac{c + 3}{(c + 2) (c - 2)} \cdot \frac{c + 2}{3 (c + 3) (c - 3)}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $c + 3$ .

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Step 3.1.1

Factor $c + 3$ out of $3 (c + 3) (c - 3)$ .

$\frac{c + 3}{(c + 2) (c - 2)} \cdot \frac{c + 2}{(c + 3) (3 (c - 3))}$

Step 3.1.2

Cancel the common factor.

$\frac{c + 3}{(c + 2) (c - 2)} \cdot \frac{c + 2}{(c + 3) (3 (c - 3))}$

Step 3.1.3

Rewrite the expression.

$\frac{1}{(c + 2) (c - 2)} \cdot \frac{c + 2}{3 (c - 3)}$

Step 3.2

Cancel the common factor of $c + 2$ .

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Step 3.2.1

Cancel the common factor.

$\frac{1}{(c + 2) (c - 2)} \cdot \frac{c + 2}{3 (c - 3)}$

Step 3.2.2

Rewrite the expression.

$\frac{1}{c - 2} \cdot \frac{1}{3 (c - 3)}$

Step 3.3

Multiply $\frac{1}{c - 2}$ by $\frac{1}{3 (c - 3)}$ .

$\frac{1}{(c - 2) (3 (c - 3))}$

Step 3.4

Move $3$ to the left of $c - 2$ .

$\frac{1}{3 (c - 2) (c - 3)}$