Algebra Examples

$\frac{- 3 x + 21}{- 2 x - 4} \cdot \frac{x^{2} - 16}{x - 7}$

Step 1

Simplify with factoring out.

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Step 1.1

Factor $3$ out of $- 3 x + 21$ .

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Step 1.1.1

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

$\frac{3 (- x) + 21}{- 2 x - 4} \cdot \frac{x^{2} - 16}{x - 7}$

Step 1.1.2

Factor $3$ out of $21$ .

$\frac{3 (- x) + 3 (7)}{- 2 x - 4} \cdot \frac{x^{2} - 16}{x - 7}$

Step 1.1.3

Factor $3$ out of $3 (- x) + 3 (7)$ .

$\frac{3 (- x + 7)}{- 2 x - 4} \cdot \frac{x^{2} - 16}{x - 7}$

Step 1.2

Factor $2$ out of $- 2 x - 4$ .

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Step 1.2.1

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

$\frac{3 (- x + 7)}{2 (- x) - 4} \cdot \frac{x^{2} - 16}{x - 7}$

Step 1.2.2

Factor $2$ out of $- 4$ .

$\frac{3 (- x + 7)}{2 (- x) + 2 (- 2)} \cdot \frac{x^{2} - 16}{x - 7}$

Step 1.2.3

Factor $2$ out of $2 (- x) + 2 (- 2)$ .

$\frac{3 (- x + 7)}{2 (- x - 2)} \cdot \frac{x^{2} - 16}{x - 7}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{3 (- x + 7)}{2 (- x - 2)} \cdot \frac{x^{2} - 4^{2}}{x - 7}$

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 $b = 4$ .

$\frac{3 (- x + 7)}{2 (- x - 2)} \cdot \frac{(x + 4) (x - 4)}{x - 7}$

Step 3

Simplify terms.

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Step 3.1

Multiply $\frac{3 (- x + 7)}{2 (- x - 2)}$ by $\frac{(x + 4) (x - 4)}{x - 7}$ .

$\frac{3 (- x + 7) ((x + 4) (x - 4))}{2 (- x - 2) (x - 7)}$

Step 3.2

Cancel the common factor of $- x + 7$ and $x - 7$ .

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Step 3.2.1

Factor $- 1$ out of $- x$ .

$\frac{3 (- (x) + 7) ((x + 4) (x - 4))}{2 (- x - 2) (x - 7)}$

Step 3.2.2

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{3 (- (x) - 1 (- 7)) ((x + 4) (x - 4))}{2 (- x - 2) (x - 7)}$

Step 3.2.3

Factor $- 1$ out of $- (x) - 1 (- 7)$ .

$\frac{3 (- (x - 7)) ((x + 4) (x - 4))}{2 (- x - 2) (x - 7)}$

Step 3.2.4

Rewrite $- (x - 7)$ as $- 1 (x - 7)$ .

$\frac{3 (- 1 (x - 7)) ((x + 4) (x - 4))}{2 (- x - 2) (x - 7)}$

Step 3.2.5

Cancel the common factor.

$\frac{3 (- 1 (x - 7)) ((x + 4) (x - 4))}{2 (- x - 2) (x - 7)}$

Step 3.2.6

Rewrite the expression.

$\frac{3 \cdot (- 1) ((x + 4) (x - 4))}{2 (- x - 2)}$

Step 3.3

Simplify the expression.

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Step 3.3.1

Multiply $3$ by $- 1$ .

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

Step 3.3.2

Move the negative in front of the fraction.

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

Step 3.4

Factor $- 1$ out of $- x$ .

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

Step 3.5

Rewrite $- 2$ as $- 1 (2)$ .

$- \frac{3 (x + 4) (x - 4)}{2 (- (x) - 1 (2))}$

Step 3.6

Factor $- 1$ out of $- (x) - 1 (2)$ .

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

Step 3.7

Simplify the expression.

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Step 3.7.1

Rewrite $- (x + 2)$ as $- 1 (x + 2)$ .

$- \frac{3 (x + 4) (x - 4)}{2 (- 1 (x + 2))}$

Step 3.7.2

Move the negative in front of the fraction.

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

Step 3.7.3

Multiply $- 1$ by $- 1$ .

$1 \frac{3 (x + 4) (x - 4)}{2 (x + 2)}$

Step 3.7.4

Multiply $\frac{3 (x + 4) (x - 4)}{2 (x + 2)}$ by $1$ .

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