Basic Math Examples

$\frac{15 b^{2}}{b^{2} - c^{2}} \div \frac{5 b}{b^{2} - 25}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{15 b^{2}}{b^{2} - c^{2}} \cdot \frac{b^{2} - 25}{5 b}$

Step 2

Cancel the common factor of $5 b$ .

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Step 2.1

Factor $5 b$ out of $15 b^{2}$ .

$\frac{5 b (3 b)}{b^{2} - c^{2}} \cdot \frac{b^{2} - 25}{5 b}$

Step 2.2

Cancel the common factor.

$\frac{5 b (3 b)}{b^{2} - c^{2}} \cdot \frac{b^{2} - 25}{5 b}$

Step 2.3

Rewrite the expression.

$\frac{3 b}{b^{2} - c^{2}} (b^{2} - 25)$

Step 3

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

$\frac{3 b}{(b + c) (b - c)} (b^{2} - 25)$

Step 4

Multiply $\frac{3 b}{(b + c) (b - c)}$ by $b^{2} - 25$ .

$\frac{3 b (b^{2} - 25)}{(b + c) (b - c)}$

Step 5

Simplify the numerator.

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Step 5.1

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

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

Step 5.2

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

$\frac{3 b (b + 5) (b - 5)}{(b + c) (b - c)}$