Algebra Examples

$\frac{42 a^{2} - 24 a}{21 a - 12} \cdot \frac{3 a - 9}{6 a^{2} + 24 a}$

Step 1

Factor $6 a$ out of $42 a^{2} - 24 a$ .

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Step 1.1

Factor $6 a$ out of $42 a^{2}$ .

$\frac{6 a (7 a) - 24 a}{21 a - 12} \cdot \frac{3 a - 9}{6 a^{2} + 24 a}$

Step 1.2

Factor $6 a$ out of $- 24 a$ .

$\frac{6 a (7 a) + 6 a (- 4)}{21 a - 12} \cdot \frac{3 a - 9}{6 a^{2} + 24 a}$

Step 1.3

Factor $6 a$ out of $6 a (7 a) + 6 a (- 4)$ .

$\frac{6 a (7 a - 4)}{21 a - 12} \cdot \frac{3 a - 9}{6 a^{2} + 24 a}$

Step 2

Factor $3$ out of $21 a - 12$ .

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Step 2.1

Factor $3$ out of $21 a$ .

$\frac{6 a (7 a - 4)}{3 (7 a) - 12} \cdot \frac{3 a - 9}{6 a^{2} + 24 a}$

Step 2.2

Factor $3$ out of $- 12$ .

$\frac{6 a (7 a - 4)}{3 (7 a) + 3 (- 4)} \cdot \frac{3 a - 9}{6 a^{2} + 24 a}$

Step 2.3

Factor $3$ out of $3 (7 a) + 3 (- 4)$ .

$\frac{6 a (7 a - 4)}{3 (7 a - 4)} \cdot \frac{3 a - 9}{6 a^{2} + 24 a}$

Step 3

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

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Step 3.1

Factor $3$ out of $3 a$ .

$\frac{6 a (7 a - 4)}{3 (7 a - 4)} \cdot \frac{3 (a) - 9}{6 a^{2} + 24 a}$

Step 3.2

Factor $3$ out of $- 9$ .

$\frac{6 a (7 a - 4)}{3 (7 a - 4)} \cdot \frac{3 a + 3 \cdot - 3}{6 a^{2} + 24 a}$

Step 3.3

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

$\frac{6 a (7 a - 4)}{3 (7 a - 4)} \cdot \frac{3 (a - 3)}{6 a^{2} + 24 a}$

Step 4

Factor $6 a$ out of $6 a^{2} + 24 a$ .

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Step 4.1

Factor $6 a$ out of $6 a^{2}$ .

$\frac{6 a (7 a - 4)}{3 (7 a - 4)} \cdot \frac{3 (a - 3)}{6 a (a) + 24 a}$

Step 4.2

Factor $6 a$ out of $24 a$ .

$\frac{6 a (7 a - 4)}{3 (7 a - 4)} \cdot \frac{3 (a - 3)}{6 a (a) + 6 a (4)}$

Step 4.3

Factor $6 a$ out of $6 a (a) + 6 a (4)$ .

$\frac{6 a (7 a - 4)}{3 (7 a - 4)} \cdot \frac{3 (a - 3)}{6 a (a + 4)}$

Step 5

Cancel the common factor of $6 a$ .

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Step 5.1

Cancel the common factor.

$\frac{6 a (7 a - 4)}{3 (7 a - 4)} \cdot \frac{3 (a - 3)}{6 a (a + 4)}$

Step 5.2

Rewrite the expression.

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

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{7 a - 4}{7 a - 4} \cdot \frac{a - 3}{a + 4}$

Step 7

Multiply $\frac{7 a - 4}{7 a - 4}$ by $\frac{a - 3}{a + 4}$ .

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

Step 8

Cancel the common factor of $7 a - 4$ .

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Step 8.1

Cancel the common factor.

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

Step 8.2

Rewrite the expression.

$\frac{a - 3}{a + 4}$