Algebra Examples

$\frac{3 x - 15}{4} \div \frac{x^{2} - 25}{2 x - 10}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 x - 15}{4} \cdot \frac{2 x - 10}{x^{2} - 25}$

Step 2

Simplify with factoring out.

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Step 2.1

Factor $3$ out of $3 x - 15$ .

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Step 2.1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 15}{4} \cdot \frac{2 x - 10}{x^{2} - 25}$

Step 2.1.2

Factor $3$ out of $- 15$ .

$\frac{3 x + 3 \cdot - 5}{4} \cdot \frac{2 x - 10}{x^{2} - 25}$

Step 2.1.3

Factor $3$ out of $3 x + 3 \cdot - 5$ .

$\frac{3 (x - 5)}{4} \cdot \frac{2 x - 10}{x^{2} - 25}$

Step 2.2

Factor $2$ out of $2 x - 10$ .

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Step 2.2.1

Factor $2$ out of $2 x$ .

$\frac{3 (x - 5)}{4} \cdot \frac{2 (x) - 10}{x^{2} - 25}$

Step 2.2.2

Factor $2$ out of $- 10$ .

$\frac{3 (x - 5)}{4} \cdot \frac{2 x + 2 \cdot - 5}{x^{2} - 25}$

Step 2.2.3

Factor $2$ out of $2 x + 2 \cdot - 5$ .

$\frac{3 (x - 5)}{4} \cdot \frac{2 (x - 5)}{x^{2} - 25}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{3 (x - 5)}{4} \cdot \frac{2 (x - 5)}{x^{2} - 5^{2}}$

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 $b = 5$ .

$\frac{3 (x - 5)}{4} \cdot \frac{2 (x - 5)}{(x + 5) (x - 5)}$

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

Factor $x - 5$ out of $3 (x - 5)$ .

$\frac{(x - 5) \cdot 3}{4} \cdot \frac{2 (x - 5)}{(x + 5) (x - 5)}$

Step 4.1.2

Factor $x - 5$ out of $(x + 5) (x - 5)$ .

$\frac{(x - 5) \cdot 3}{4} \cdot \frac{2 (x - 5)}{(x - 5) (x + 5)}$

Step 4.1.3

Cancel the common factor.

$\frac{(x - 5) \cdot 3}{4} \cdot \frac{2 (x - 5)}{(x - 5) (x + 5)}$

Step 4.1.4

Rewrite the expression.

$\frac{3}{4} \cdot \frac{2 (x - 5)}{x + 5}$

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Factor $2$ out of $4$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$\frac{3}{2} \cdot \frac{x - 5}{x + 5}$

Step 4.3

Multiply $\frac{3}{2}$ by $\frac{x - 5}{x + 5}$ .

$\frac{3 (x - 5)}{2 (x + 5)}$