Basic Math Examples

$\frac{3 c - 9}{4 c^{2} - 6 c} \div \frac{5 c^{2} - 15 c}{12 c^{3} - 18 c^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 c - 9}{4 c^{2} - 6 c} \cdot \frac{12 c^{3} - 18 c^{2}}{5 c^{2} - 15 c}$

Step 2

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

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Step 2.1

Factor $3$ out of $3 c$ .

$\frac{3 (c) - 9}{4 c^{2} - 6 c} \cdot \frac{12 c^{3} - 18 c^{2}}{5 c^{2} - 15 c}$

Step 2.2

Factor $3$ out of $- 9$ .

$\frac{3 c + 3 \cdot - 3}{4 c^{2} - 6 c} \cdot \frac{12 c^{3} - 18 c^{2}}{5 c^{2} - 15 c}$

Step 2.3

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

$\frac{3 (c - 3)}{4 c^{2} - 6 c} \cdot \frac{12 c^{3} - 18 c^{2}}{5 c^{2} - 15 c}$

Step 3

Factor $2 c$ out of $4 c^{2} - 6 c$ .

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Step 3.1

Factor $2 c$ out of $4 c^{2}$ .

$\frac{3 (c - 3)}{2 c (2 c) - 6 c} \cdot \frac{12 c^{3} - 18 c^{2}}{5 c^{2} - 15 c}$

Step 3.2

Factor $2 c$ out of $- 6 c$ .

$\frac{3 (c - 3)}{2 c (2 c) + 2 c (- 3)} \cdot \frac{12 c^{3} - 18 c^{2}}{5 c^{2} - 15 c}$

Step 3.3

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

$\frac{3 (c - 3)}{2 c (2 c - 3)} \cdot \frac{12 c^{3} - 18 c^{2}}{5 c^{2} - 15 c}$

Step 4

Factor $6 c^{2}$ out of $12 c^{3} - 18 c^{2}$ .

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Step 4.1

Factor $6 c^{2}$ out of $12 c^{3}$ .

$\frac{3 (c - 3)}{2 c (2 c - 3)} \cdot \frac{6 c^{2} (2 c) - 18 c^{2}}{5 c^{2} - 15 c}$

Step 4.2

Factor $6 c^{2}$ out of $- 18 c^{2}$ .

$\frac{3 (c - 3)}{2 c (2 c - 3)} \cdot \frac{6 c^{2} (2 c) + 6 c^{2} (- 3)}{5 c^{2} - 15 c}$

Step 4.3

Factor $6 c^{2}$ out of $6 c^{2} (2 c) + 6 c^{2} (- 3)$ .

$\frac{3 (c - 3)}{2 c (2 c - 3)} \cdot \frac{6 c^{2} (2 c - 3)}{5 c^{2} - 15 c}$

Step 5

Factor $5 c$ out of $5 c^{2} - 15 c$ .

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Step 5.1

Factor $5 c$ out of $5 c^{2}$ .

$\frac{3 (c - 3)}{2 c (2 c - 3)} \cdot \frac{6 c^{2} (2 c - 3)}{5 c (c) - 15 c}$

Step 5.2

Factor $5 c$ out of $- 15 c$ .

$\frac{3 (c - 3)}{2 c (2 c - 3)} \cdot \frac{6 c^{2} (2 c - 3)}{5 c (c) + 5 c (- 3)}$

Step 5.3

Factor $5 c$ out of $5 c (c) + 5 c (- 3)$ .

$\frac{3 (c - 3)}{2 c (2 c - 3)} \cdot \frac{6 c^{2} (2 c - 3)}{5 c (c - 3)}$

Step 6

Combine.

$\frac{3 (c - 3) (6 c^{2} (2 c - 3))}{2 c (2 c - 3) (5 c (c - 3))}$

Step 7

Multiply $c$ by $c$ by adding the exponents.

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Step 7.1

Move $c$ .

$\frac{3 (c - 3) (6 c^{2} (2 c - 3))}{2 (c \cdot c) (2 c - 3) (5 (c - 3))}$

Step 7.2

Multiply $c$ by $c$ .

$\frac{3 (c - 3) (6 c^{2} (2 c - 3))}{2 c^{2} (2 c - 3) (5 (c - 3))}$

Step 8

Reduce the expression by cancelling the common factors.

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Step 8.1

Cancel the common factor of $c - 3$ .

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Step 8.1.1

Cancel the common factor.

$\frac{3 (c - 3) (6 c^{2} (2 c - 3))}{2 c^{2} (2 c - 3) (5 (c - 3))}$

Step 8.1.2

Rewrite the expression.

$\frac{3 (6 c^{2} (2 c - 3))}{2 c^{2} (2 c - 3) \cdot (5)}$

Step 8.2

Cancel the common factor of $6$ and $2$ .

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Step 8.2.1

Factor $2$ out of $3 (6 c^{2} (2 c - 3))$ .

$\frac{2 (3 (3 c^{2} (2 c - 3)))}{2 c^{2} (2 c - 3) \cdot (5)}$

Step 8.2.2

Cancel the common factors.

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Step 8.2.2.1

Factor $2$ out of $2 c^{2} (2 c - 3) \cdot (5)$ .

$\frac{2 (3 (3 c^{2} (2 c - 3)))}{2 ((c^{2} (2 c - 3)) \cdot (5))}$

Step 8.2.2.2

Cancel the common factor.

$\frac{2 (3 (3 c^{2} (2 c - 3)))}{2 ((c^{2} (2 c - 3)) \cdot (5))}$

Step 8.2.2.3

Rewrite the expression.

$\frac{3 (3 c^{2} (2 c - 3))}{(c^{2} (2 c - 3)) \cdot (5)}$

Step 8.3

Cancel the common factor of $c^{2}$ .

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Step 8.3.1

Cancel the common factor.

$\frac{3 (3 c^{2} (2 c - 3))}{c^{2} (2 c - 3) \cdot 5}$

Step 8.3.2

Rewrite the expression.

$\frac{3 (3 (2 c - 3))}{(2 c - 3) \cdot (5)}$

Step 8.4

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

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Step 8.4.1

Cancel the common factor.

$\frac{3 (3 (2 c - 3))}{(2 c - 3) \cdot 5}$

Step 8.4.2

Rewrite the expression.

$\frac{3 \cdot (3)}{5}$

Step 9

Multiply $3$ by $3$ .

$\frac{9}{5}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{5}$

Decimal Form:

$1.8$

Mixed Number Form:

$1 \frac{4}{5}$