Basic Math Examples

$\frac{c^{2} + 7 c + 12}{c - 9} \div \frac{c^{2} - 2 c - 24}{c - 9}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{c^{2} + 7 c + 12}{c - 9} \cdot \frac{c - 9}{c^{2} - 2 c - 24}$

Step 2

Cancel the common factor of $c - 9$ .

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Step 2.1

Cancel the common factor.

$\frac{c^{2} + 7 c + 12}{c - 9} \cdot \frac{c - 9}{c^{2} - 2 c - 24}$

Step 2.2

Rewrite the expression.

$(c^{2} + 7 c + 12) \frac{1}{c^{2} - 2 c - 24}$

Step 3

Factor $c^{2} - 2 c - 24$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 24$ and whose sum is $- 2$ .

$- 6, 4$

Step 3.2

Write the factored form using these integers.

$(c^{2} + 7 c + 12) \frac{1}{(c - 6) (c + 4)}$

Step 4

Multiply $c^{2} + 7 c + 12$ by $\frac{1}{(c - 6) (c + 4)}$ .

$\frac{c^{2} + 7 c + 12}{(c - 6) (c + 4)}$

Step 5

Factor $c^{2} + 7 c + 12$ using the AC method.

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Step 5.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $12$ and whose sum is $7$ .

$3, 4$

Step 5.2

Write the factored form using these integers.

$\frac{(c + 3) (c + 4)}{(c - 6) (c + 4)}$

Step 6

Cancel the common factor of $c + 4$ .

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Step 6.1

Cancel the common factor.

$\frac{(c + 3) (c + 4)}{(c - 6) (c + 4)}$

Step 6.2

Rewrite the expression.

$\frac{c + 3}{c - 6}$