Algebra Examples

$\frac{3 x - 9}{9 x^{2} - 4} \cdot \frac{3 x - 2}{5 x + 7}$

Step 1

Factor $3$ out of $3 x - 9$ .

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Step 1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 9}{9 x^{2} - 4} \cdot \frac{3 x - 2}{5 x + 7}$

Step 1.2

Factor $3$ out of $- 9$ .

$\frac{3 x + 3 \cdot - 3}{9 x^{2} - 4} \cdot \frac{3 x - 2}{5 x + 7}$

Step 1.3

Factor $3$ out of $3 x + 3 \cdot - 3$ .

$\frac{3 (x - 3)}{9 x^{2} - 4} \cdot \frac{3 x - 2}{5 x + 7}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$\frac{3 (x - 3)}{{(3 x)}^{2} - 4} \cdot \frac{3 x - 2}{5 x + 7}$

Step 2.2

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

$\frac{3 (x - 3)}{{(3 x)}^{2} - 2^{2}} \cdot \frac{3 x - 2}{5 x + 7}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 x$ and $b = 2$ .

$\frac{3 (x - 3)}{(3 x + 2) (3 x - 2)} \cdot \frac{3 x - 2}{5 x + 7}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $3 x - 2$ .

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Step 3.1.1

Factor $3 x - 2$ out of $(3 x + 2) (3 x - 2)$ .

$\frac{3 (x - 3)}{(3 x - 2) (3 x + 2)} \cdot \frac{3 x - 2}{5 x + 7}$

Step 3.1.2

Cancel the common factor.

$\frac{3 (x - 3)}{(3 x - 2) (3 x + 2)} \cdot \frac{3 x - 2}{5 x + 7}$

Step 3.1.3

Rewrite the expression.

$\frac{3 (x - 3)}{3 x + 2} \cdot \frac{1}{5 x + 7}$

Step 3.2

Multiply $\frac{3 (x - 3)}{3 x + 2}$ by $\frac{1}{5 x + 7}$ .

$\frac{3 (x - 3)}{(3 x + 2) (5 x + 7)}$