Precalculus Examples

$(\frac{4 a}{3 (a - 4)}) (\frac{9 (a - 4)}{16 a^{2}})$

Step 1

Combine.

$\frac{4 a (9 (a - 4))}{3 (a - 4) (16 a^{2})}$

Step 2

Cancel the common factor of $4$ and $16$ .

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Step 2.1

Factor $4$ out of $4 a (9 (a - 4))$ .

$\frac{4 (a (9 (a - 4)))}{3 (a - 4) (16 a^{2})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $3 (a - 4) (16 a^{2})$ .

$\frac{4 (a (9 (a - 4)))}{4 (3 (a - 4) (4 a^{2}))}$

Step 2.2.2

Cancel the common factor.

$\frac{4 (a (9 (a - 4)))}{4 (3 (a - 4) (4 a^{2}))}$

Step 2.2.3

Rewrite the expression.

$\frac{a (9 (a - 4))}{3 (a - 4) (4 a^{2})}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $a$ out of $3 (a - 4) (4 a^{2})$ .

$\frac{a (9 (a - 4))}{a (3 (a - 4) (4 a))}$

Step 3.2

Cancel the common factor.

$\frac{a (9 (a - 4))}{a (3 (a - 4) (4 a))}$

Step 3.3

Rewrite the expression.

$\frac{9 (a - 4)}{3 (a - 4) (4 a)}$

Step 4

Cancel the common factor of $9$ and $3$ .

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Step 4.1

Factor $3$ out of $9 (a - 4)$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Cancel the common factor of $a - 4$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\frac{3}{4 a}$