Trigonometry Examples

$\frac{6 x - 42}{- 7 x} \cdot \frac{77}{63 - 9 x}$

Step 1

Simplify terms.

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Step 1.1

Factor $6$ out of $6 x - 42$ .

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Step 1.1.1

Factor $6$ out of $6 x$ .

$\frac{6 (x) - 42}{- 7 x} \cdot \frac{77}{63 - 9 x}$

Step 1.1.2

Factor $6$ out of $- 42$ .

$\frac{6 x + 6 \cdot - 7}{- 7 x} \cdot \frac{77}{63 - 9 x}$

Step 1.1.3

Factor $6$ out of $6 x + 6 \cdot - 7$ .

$\frac{6 (x - 7)}{- 7 x} \cdot \frac{77}{63 - 9 x}$

Step 1.2

Factor $9$ out of $63 - 9 x$ .

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Step 1.2.1

Factor $9$ out of $63$ .

$\frac{6 (x - 7)}{- 7 x} \cdot \frac{77}{9 (7) - 9 x}$

Step 1.2.2

Factor $9$ out of $- 9 x$ .

$\frac{6 (x - 7)}{- 7 x} \cdot \frac{77}{9 (7) + 9 (- x)}$

Step 1.2.3

Factor $9$ out of $9 (7) + 9 (- x)$ .

$\frac{6 (x - 7)}{- 7 x} \cdot \frac{77}{9 (7 - x)}$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Factor $3$ out of $6 (x - 7)$ .

$\frac{3 (2 (x - 7))}{- 7 x} \cdot \frac{77}{9 (7 - x)}$

Step 1.3.2

Factor $3$ out of $9 (7 - x)$ .

$\frac{3 (2 (x - 7))}{- 7 x} \cdot \frac{77}{3 (3 (7 - x))}$

Step 1.3.3

Cancel the common factor.

$\frac{3 (2 (x - 7))}{- 7 x} \cdot \frac{77}{3 (3 (7 - x))}$

Step 1.3.4

Rewrite the expression.

$\frac{2 (x - 7)}{- 7 x} \cdot \frac{77}{3 (7 - x)}$

Step 1.4

Cancel the common factor of $7$ .

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Step 1.4.1

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

$\frac{2 (x - 7)}{7 (- x)} \cdot \frac{77}{3 (7 - x)}$

Step 1.4.2

Factor $7$ out of $77$ .

$\frac{2 (x - 7)}{7 (- x)} \cdot \frac{7 (11)}{3 (7 - x)}$

Step 1.4.3

Cancel the common factor.

$\frac{2 (x - 7)}{7 (- x)} \cdot \frac{7 \cdot 11}{3 (7 - x)}$

Step 1.4.4

Rewrite the expression.

$\frac{2 (x - 7)}{- x} \cdot \frac{11}{3 (7 - x)}$

Step 1.5

Multiply $\frac{2 (x - 7)}{- x}$ by $\frac{11}{3 (7 - x)}$ .

$\frac{2 (x - 7) \cdot 11}{- x (3 (7 - x))}$

Step 1.6

Multiply.

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Step 1.6.1

Multiply $11$ by $2$ .

$\frac{22 (x - 7)}{- x (3 (7 - x))}$

Step 1.6.2

Multiply $3$ by $- 1$ .

$\frac{22 (x - 7)}{- 3 x (7 - x)}$

Step 1.7

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

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Step 1.7.1

Factor $- 1$ out of $x$ .

$\frac{22 (- 1 (- x) - 7)}{- 3 x (7 - x)}$

Step 1.7.2

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

$\frac{22 (- 1 (- x) - 1 (7))}{- 3 x (7 - x)}$

Step 1.7.3

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

$\frac{22 (- 1 (- x + 7))}{- 3 x (7 - x)}$

Step 1.7.4

Reorder terms.

$\frac{22 (- 1 (- x + 7))}{- 3 x (- x + 7)}$

Step 1.7.5

Cancel the common factor.

$\frac{22 (- 1 (- x + 7))}{- 3 x (- x + 7)}$

Step 1.7.6

Rewrite the expression.

$\frac{22 \cdot (- 1)}{- 3 x}$

Step 2

Multiply $22$ by $- 1$ .

$\frac{- 22}{- 3 x}$

Step 3

Dividing two negative values results in a positive value.

$\frac{22}{3 x}$