Basic Math Examples

$\frac{c^{2} + 3 c}{a^{2} - 2 a} \cdot \frac{c a^{2} - 2 c a}{c^{2} - 9} \div \frac{a^{2}}{c - 3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{c^{2} + 3 c}{a^{2} - 2 a} \cdot \frac{c a^{2} - 2 c a}{c^{2} - 9} \frac{c - 3}{a^{2}}$

Step 2

Simplify with factoring out.

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Step 2.1

Factor $c$ out of $c^{2} + 3 c$ .

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Step 2.1.1

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

$\frac{c \cdot c + 3 c}{a^{2} - 2 a} \cdot \frac{c a^{2} - 2 c a}{c^{2} - 9} \frac{c - 3}{a^{2}}$

Step 2.1.2

Factor $c$ out of $3 c$ .

$\frac{c \cdot c + c \cdot 3}{a^{2} - 2 a} \cdot \frac{c a^{2} - 2 c a}{c^{2} - 9} \frac{c - 3}{a^{2}}$

Step 2.1.3

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

$\frac{c (c + 3)}{a^{2} - 2 a} \cdot \frac{c a^{2} - 2 c a}{c^{2} - 9} \frac{c - 3}{a^{2}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{c (c + 3)}{a \cdot a - 2 a} \cdot \frac{c a^{2} - 2 c a}{c^{2} - 9} \frac{c - 3}{a^{2}}$

Step 2.2.2

Factor $a$ out of $- 2 a$ .

$\frac{c (c + 3)}{a \cdot a + a \cdot - 2} \cdot \frac{c a^{2} - 2 c a}{c^{2} - 9} \frac{c - 3}{a^{2}}$

Step 2.2.3

Factor $a$ out of $a \cdot a + a \cdot - 2$ .

$\frac{c (c + 3)}{a (a - 2)} \cdot \frac{c a^{2} - 2 c a}{c^{2} - 9} \frac{c - 3}{a^{2}}$

Step 2.3

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

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Step 2.3.1

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

$\frac{c (c + 3)}{a (a - 2)} \cdot \frac{c a (a) - 2 c a}{c^{2} - 9} \frac{c - 3}{a^{2}}$

Step 2.3.2

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

$\frac{c (c + 3)}{a (a - 2)} \cdot \frac{c a (a) + c a (- 2)}{c^{2} - 9} \frac{c - 3}{a^{2}}$

Step 2.3.3

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

$\frac{c (c + 3)}{a (a - 2)} \cdot \frac{c a (a - 2)}{c^{2} - 9} \frac{c - 3}{a^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $9$ as $3^{2}$ .

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

Step 3.2

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

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

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $c + 3$ .

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Step 4.1.1

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

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

Step 4.1.2

Cancel the common factor.

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

Step 4.1.3

Rewrite the expression.

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

Step 4.2

Cancel the common factor of $a (a - 2)$ .

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Step 4.2.1

Factor $a (a - 2)$ out of $c a (a - 2)$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$c \cdot \frac{c}{c - 3} \frac{c - 3}{a^{2}}$

Step 4.3

Combine $c$ and $\frac{c}{c - 3}$ .

$\frac{c \cdot c}{c - 3} \cdot \frac{c - 3}{a^{2}}$

Step 5

Raise $c$ to the power of $1$ .

$\frac{c^{1} c}{c - 3} \cdot \frac{c - 3}{a^{2}}$

Step 6

Raise $c$ to the power of $1$ .

$\frac{c^{1} c^{1}}{c - 3} \cdot \frac{c - 3}{a^{2}}$

Step 7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{c^{1 + 1}}{c - 3} \cdot \frac{c - 3}{a^{2}}$

Step 8

Add $1$ and $1$ .

$\frac{c^{2}}{c - 3} \cdot \frac{c - 3}{a^{2}}$

Step 9

Cancel the common factor of $c - 3$ .

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Step 9.1

Cancel the common factor.

$\frac{c^{2}}{c - 3} \cdot \frac{c - 3}{a^{2}}$

Step 9.2

Rewrite the expression.

$c^{2} \frac{1}{a^{2}}$

Step 10

Combine $c^{2}$ and $\frac{1}{a^{2}}$ .

$\frac{c^{2}}{a^{2}}$