Simplify ((x^2-49)/(x+8)*(x^2+8x)/(x+7))÷((x^2-7x)/14)

$\frac{x^{2} - 49}{x + 8} \cdot \frac{x^{2} + 8 x}{x + 7} \div \frac{x^{2} - 7 x}{14}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 49}{x + 8} \cdot \frac{x^{2} + 8 x}{x + 7} \frac{14}{x^{2} - 7 x}$

Simplify the numerator.

Rewrite $49$ as $7^{2}$ .

$\frac{x^{2} - 7^{2}}{x + 8} \cdot \frac{x^{2} + 8 x}{x + 7} \frac{14}{x^{2} - 7 x}$

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 $b = 7$ .

$\frac{(x + 7) (x - 7)}{x + 8} \cdot \frac{x^{2} + 8 x}{x + 7} \frac{14}{x^{2} - 7 x}$

Simplify terms.

Factor $x$ out of $x^{2} + 8 x$ .

Factor $x$ out of $x^{2}$ .

$\frac{(x + 7) (x - 7)}{x + 8} \cdot \frac{x \cdot x + 8 x}{x + 7} \frac{14}{x^{2} - 7 x}$

Factor $x$ out of $8 x$ .

$\frac{(x + 7) (x - 7)}{x + 8} \cdot \frac{x \cdot x + x \cdot 8}{x + 7} \frac{14}{x^{2} - 7 x}$

Factor $x$ out of $x \cdot x + x \cdot 8$ .

$\frac{(x + 7) (x - 7)}{x + 8} \cdot \frac{x (x + 8)}{x + 7} \frac{14}{x^{2} - 7 x}$

Cancel the common factor of $x + 7$ .

Cancel the common factor.

$\frac{(x + 7) (x - 7)}{x + 8} \cdot \frac{x (x + 8)}{x + 7} \frac{14}{x^{2} - 7 x}$

Rewrite the expression.

$\frac{x - 7}{x + 8} \cdot (x (x + 8)) \frac{14}{x^{2} - 7 x}$

Cancel the common factor of $x + 8$ .

Factor $x + 8$ out of $x (x + 8)$ .

$\frac{x - 7}{x + 8} \cdot ((x + 8) x) \frac{14}{x^{2} - 7 x}$

Cancel the common factor.

$\frac{x - 7}{x + 8} \cdot ((x + 8) x) \frac{14}{x^{2} - 7 x}$

Rewrite the expression.

$(x - 7) \cdot x \frac{14}{x^{2} - 7 x}$

Apply the distributive property.

$(x \cdot x - 7 x) \frac{14}{x^{2} - 7 x}$

Multiply $x$ by $x$ .

$(x^{2} - 7 x) \frac{14}{x^{2} - 7 x}$

Factor $x$ out of $x^{2} - 7 x$ .

Factor $x$ out of $x^{2}$ .

$(x^{2} - 7 x) \frac{14}{x \cdot x - 7 x}$

Factor $x$ out of $- 7 x$ .

$(x^{2} - 7 x) \frac{14}{x \cdot x + x \cdot - 7}$

Factor $x$ out of $x \cdot x + x \cdot - 7$ .

$(x^{2} - 7 x) \frac{14}{x (x - 7)}$

Multiply $x^{2} - 7 x$ by $\frac{14}{x (x - 7)}$ .

$\frac{(x^{2} - 7 x) \cdot 14}{x (x - 7)}$

Factor $x$ out of $x^{2} - 7 x$ .

Factor $x$ out of $x^{2}$ .

$\frac{(x \cdot x - 7 x) \cdot 14}{x (x - 7)}$

Factor $x$ out of $- 7 x$ .

$\frac{(x \cdot x + x \cdot - 7) \cdot 14}{x (x - 7)}$

Factor $x$ out of $x \cdot x + x \cdot - 7$ .

$\frac{x (x - 7) \cdot 14}{x (x - 7)}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x (x - 7) \cdot 14}{x (x - 7)}$

Rewrite the expression.

$\frac{(x - 7) \cdot 14}{x - 7}$

Cancel the common factor of $x - 7$ .

Cancel the common factor.

$\frac{(x - 7) \cdot 14}{x - 7}$

Divide $14$ by $1$ .

$14$

Simplify ((x^2-49)/(x+8)*(x^2+8x)/(x+7))÷((x^2-7x)/14)

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