Basic Math Examples

$\frac{\frac{c + 3}{c^{2} - 4}}{\frac{7 c + 21}{5 c^{2} + 10 c}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{c + 3}{c^{2} - 4} \cdot \frac{5 c^{2} + 10 c}{7 c + 21}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{c + 3}{c^{2} - 2^{2}} \cdot \frac{5 c^{2} + 10 c}{7 c + 21}$

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 $b = 2$ .

$\frac{c + 3}{(c + 2) (c - 2)} \cdot \frac{5 c^{2} + 10 c}{7 c + 21}$

Step 3

Simplify terms.

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Step 3.1

Factor $5 c$ out of $5 c^{2} + 10 c$ .

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Step 3.1.1

Factor $5 c$ out of $5 c^{2}$ .

$\frac{c + 3}{(c + 2) (c - 2)} \cdot \frac{5 c (c) + 10 c}{7 c + 21}$

Step 3.1.2

Factor $5 c$ out of $10 c$ .

$\frac{c + 3}{(c + 2) (c - 2)} \cdot \frac{5 c (c) + 5 c (2)}{7 c + 21}$

Step 3.1.3

Factor $5 c$ out of $5 c (c) + 5 c (2)$ .

$\frac{c + 3}{(c + 2) (c - 2)} \cdot \frac{5 c (c + 2)}{7 c + 21}$

Step 3.2

Factor $7$ out of $7 c + 21$ .

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Step 3.2.1

Factor $7$ out of $7 c$ .

$\frac{c + 3}{(c + 2) (c - 2)} \cdot \frac{5 c (c + 2)}{7 (c) + 21}$

Step 3.2.2

Factor $7$ out of $21$ .

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

Step 3.2.3

Factor $7$ out of $7 c + 7 \cdot 3$ .

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

Step 3.3

Cancel the common factor of $c + 3$ .

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Step 3.3.1

Factor $c + 3$ out of $7 (c + 3)$ .

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

Step 3.3.2

Cancel the common factor.

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

Step 3.3.3

Rewrite the expression.

$\frac{1}{(c + 2) (c - 2)} \cdot \frac{5 c (c + 2)}{7}$

Step 3.4

Cancel the common factor of $c + 2$ .

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Step 3.4.1

Factor $c + 2$ out of $5 c (c + 2)$ .

$\frac{1}{(c + 2) (c - 2)} \cdot \frac{(c + 2) (5 c)}{7}$

Step 3.4.2

Cancel the common factor.

$\frac{1}{(c + 2) (c - 2)} \cdot \frac{(c + 2) (5 c)}{7}$

Step 3.4.3

Rewrite the expression.

$\frac{1}{c - 2} \cdot \frac{5 c}{7}$

Step 3.5

Multiply $\frac{1}{c - 2}$ by $\frac{5 c}{7}$ .

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

Step 3.6

Move $7$ to the left of $c - 2$ .

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