Precalculus Examples

$\frac{6 x + 30}{7 x^{3}} \cdot \frac{x}{x^{2} - 25}$

Step 1

Factor $6$ out of $6 x + 30$ .

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Step 1.1

Factor $6$ out of $6 x$ .

$\frac{6 (x) + 30}{7 x^{3}} \cdot \frac{x}{x^{2} - 25}$

Step 1.2

Factor $6$ out of $30$ .

$\frac{6 x + 6 \cdot 5}{7 x^{3}} \cdot \frac{x}{x^{2} - 25}$

Step 1.3

Factor $6$ out of $6 x + 6 \cdot 5$ .

$\frac{6 (x + 5)}{7 x^{3}} \cdot \frac{x}{x^{2} - 25}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{6 (x + 5)}{7 x^{3}} \cdot \frac{x}{x^{2} - 5^{2}}$

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 $a = x$ and $b = 5$ .

$\frac{6 (x + 5)}{7 x^{3}} \cdot \frac{x}{(x + 5) (x - 5)}$

Step 3

Simplify terms.

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Step 3.1

Combine.

$\frac{6 (x + 5) x}{7 x^{3} ((x + 5) (x - 5))}$

Step 3.2

Cancel the common factor of $x + 5$ .

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Step 3.2.1

Cancel the common factor.

$\frac{6 (x + 5) x}{7 x^{3} ((x + 5) (x - 5))}$

Step 3.2.2

Rewrite the expression.

$\frac{6 x}{7 x^{3} (x - 5)}$

Step 3.3

Cancel the common factor of $x$ and $x^{3}$ .

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Step 3.3.1

Factor $x$ out of $6 x$ .

$\frac{x \cdot 6}{7 x^{3} (x - 5)}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $x$ out of $7 x^{3} (x - 5)$ .

$\frac{x \cdot 6}{x (7 x^{2} (x - 5))}$

Step 3.3.2.2

Cancel the common factor.

$\frac{x \cdot 6}{x (7 x^{2} (x - 5))}$

Step 3.3.2.3

Rewrite the expression.

$\frac{6}{7 x^{2} (x - 5)}$