Algebra Examples

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

Step 1

Factor $a$ out of $a^{2} - 4 a$ .

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Step 1.1

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

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

Step 1.2

Factor $a$ out of $- 4 a$ .

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

Step 1.3

Factor $a$ out of $a \cdot a + a \cdot - 4$ .

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

Step 2

Combine.

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

Step 3

Cancel the common factor of $a - 4$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{(a + 3) (2 a^{2})}{a ((a + 3) (a - 1))}$

Step 4

Cancel the common factor of $a + 3$ .

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Step 4.1

Cancel the common factor.

$\frac{(a + 3) (2 a^{2})}{a ((a + 3) (a - 1))}$

Step 4.2

Rewrite the expression.

$\frac{2 a^{2}}{a (a - 1)}$

Step 5

Cancel the common factor of $a^{2}$ and $a$ .

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Step 5.1

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

$\frac{a (2 a)}{a (a - 1)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Cancel the common factor.

$\frac{a (2 a)}{a (a - 1)}$

Step 5.2.2

Rewrite the expression.

$\frac{2 a}{a - 1}$