Trigonometry Examples

$\frac{\frac{x^{2} - 81}{48 x + 441}}{\frac{x - 9}{63}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{2} - 81}{48 x + 441} \cdot \frac{63}{x - 9}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $81$ as $9^{2}$ .

$\frac{x^{2} - 9^{2}}{48 x + 441} \cdot \frac{63}{x - 9}$

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 $b = 9$ .

$\frac{(x + 9) (x - 9)}{48 x + 441} \cdot \frac{63}{x - 9}$

Step 3

Factor $3$ out of $48 x + 441$ .

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Step 3.1

Factor $3$ out of $48 x$ .

$\frac{(x + 9) (x - 9)}{3 (16 x) + 441} \cdot \frac{63}{x - 9}$

Step 3.2

Factor $3$ out of $441$ .

$\frac{(x + 9) (x - 9)}{3 (16 x) + 3 (147)} \cdot \frac{63}{x - 9}$

Step 3.3

Factor $3$ out of $3 (16 x) + 3 (147)$ .

$\frac{(x + 9) (x - 9)}{3 (16 x + 147)} \cdot \frac{63}{x - 9}$

Step 4

Cancel the common factor of $x - 9$ .

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Step 4.1

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

$\frac{(x - 9) (x + 9)}{3 (16 x + 147)} \cdot \frac{63}{x - 9}$

Step 4.2

Cancel the common factor.

$\frac{(x - 9) (x + 9)}{3 (16 x + 147)} \cdot \frac{63}{x - 9}$

Step 4.3

Rewrite the expression.

$\frac{x + 9}{3 (16 x + 147)} \cdot 63$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $63$ .

$\frac{x + 9}{3 (16 x + 147)} \cdot (3 (21))$

Step 5.2

Cancel the common factor.

$\frac{x + 9}{3 (16 x + 147)} \cdot (3 \cdot 21)$

Step 5.3

Rewrite the expression.

$\frac{x + 9}{16 x + 147} \cdot 21$

Step 6

Combine $\frac{x + 9}{16 x + 147}$ and $21$ .

$\frac{(x + 9) \cdot 21}{16 x + 147}$

Step 7

Move $21$ to the left of $x + 9$ .

$\frac{21 (x + 9)}{16 x + 147}$