Basic Math Examples

$\frac{c^{2} - c - 6}{c^{2} + 4 c + 3} \div \frac{c - 3}{3 c + 3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{c^{2} - c - 6}{c^{2} + 4 c + 3} \cdot \frac{3 c + 3}{c - 3}$

Step 2

Factor $c^{2} - c - 6$ using the AC method.

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Step 2.1

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 $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Step 2.2

Write the factored form using these integers.

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

Step 3

Factor $c^{2} + 4 c + 3$ 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 $3$ and whose sum is $4$ .

$1, 3$

Step 3.2

Write the factored form using these integers.

$\frac{(c - 3) (c + 2)}{(c + 1) (c + 3)} \cdot \frac{3 c + 3}{c - 3}$

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

Cancel the common factor.

$\frac{(c - 3) (c + 2)}{(c + 1) (c + 3)} \cdot \frac{3 c + 3}{c - 3}$

Step 4.1.2

Rewrite the expression.

$\frac{c + 2}{(c + 1) (c + 3)} (3 c + 3)$

Step 4.2

Multiply $\frac{c + 2}{(c + 1) (c + 3)}$ by $3 c + 3$ .

$\frac{(c + 2) (3 c + 3)}{(c + 1) (c + 3)}$

Step 5

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

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Step 5.1

Factor $3$ out of $3 c$ .

$\frac{(c + 2) (3 (c) + 3)}{(c + 1) (c + 3)}$

Step 5.2

Factor $3$ out of $3$ .

$\frac{(c + 2) (3 (c) + 3 (1))}{(c + 1) (c + 3)}$

Step 5.3

Factor $3$ out of $3 (c) + 3 (1)$ .

$\frac{(c + 2) (3 (c + 1))}{(c + 1) (c + 3)}$

$\frac{(c + 2) \cdot 3 (c + 1)}{(c + 1) (c + 3)}$

Step 6

Cancel the common factor of $c + 1$ .

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Step 6.1

Cancel the common factor.

$\frac{(c + 2) \cdot 3 (c + 1)}{(c + 1) (c + 3)}$

Step 6.2

Rewrite the expression.

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

Step 7

Move $3$ to the left of $c + 2$ .

$\frac{3 (c + 2)}{c + 3}$