Trigonometry Examples

$\frac{x^{2} - 25}{14} \div \frac{x - 5}{28}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 25}{14} \cdot \frac{28}{x - 5}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $14$ .

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Step 2.1.1

Factor $14$ out of $28$ .

$\frac{x^{2} - 25}{14} \cdot \frac{14 (2)}{x - 5}$

Step 2.1.2

Cancel the common factor.

$\frac{x^{2} - 25}{14} \cdot \frac{14 \cdot 2}{x - 5}$

Step 2.1.3

Rewrite the expression.

$(x^{2} - 25) \frac{2}{x - 5}$

Step 2.2

Multiply $x^{2} - 25$ by $\frac{2}{x - 5}$ .

$\frac{(x^{2} - 25) \cdot 2}{x - 5}$

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{(x^{2} - 5^{2}) \cdot 2}{x - 5}$

Step 3.2

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

$\frac{(x + 5) (x - 5) \cdot 2}{x - 5}$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $x - 5$ .

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Step 4.1.1

Cancel the common factor.

$\frac{(x + 5) (x - 5) \cdot 2}{x - 5}$

Step 4.1.2

Divide $(x + 5) \cdot 2$ by $1$ .

$(x + 5) \cdot 2$

Step 4.2

Apply the distributive property.

$x \cdot 2 + 5 \cdot 2$

Step 4.3

Simplify the expression.

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Step 4.3.1

Move $2$ to the left of $x$ .

$2 \cdot x + 5 \cdot 2$

Step 4.3.2

Multiply $5$ by $2$ .

$2 x + 10$