Algebra Examples

$\frac{x^{2} - 16}{6 x} \cdot \frac{7 x}{x + 4}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $16$ as $4^{2}$ .

$\frac{x^{2} - 4^{2}}{6 x} \cdot \frac{7 x}{x + 4}$

Step 1.2

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 $b = 4$ .

$\frac{(x + 4) (x - 4)}{6 x} \cdot \frac{7 x}{x + 4}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $x + 4$ .

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Step 2.1.1

Cancel the common factor.

$\frac{(x + 4) (x - 4)}{6 x} \cdot \frac{7 x}{x + 4}$

Step 2.1.2

Rewrite the expression.

$\frac{x - 4}{6 x} \cdot (7 x)$

Step 2.2

Cancel the common factor of $x$ .

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Step 2.2.1

Factor $x$ out of $6 x$ .

$\frac{x - 4}{x \cdot 6} \cdot (7 x)$

Step 2.2.2

Factor $x$ out of $7 x$ .

$\frac{x - 4}{x \cdot 6} \cdot (x \cdot 7)$

Step 2.2.3

Cancel the common factor.

$\frac{x - 4}{x \cdot 6} \cdot (x \cdot 7)$

Step 2.2.4

Rewrite the expression.

$\frac{x - 4}{6} \cdot 7$

Step 2.3

Combine $\frac{x - 4}{6}$ and $7$ .

$\frac{(x - 4) \cdot 7}{6}$

Step 2.4

Move $7$ to the left of $x - 4$ .

$\frac{7 (x - 4)}{6}$