Basic Math Examples

$\frac{4 c}{2 c + 2} \cdot \frac{c^{2} + 3 c + 2}{c - 1}$

Step 1

Factor $2$ out of $2 c + 2$ .

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Step 1.1

Factor $2$ out of $2 c$ .

$\frac{4 c}{2 (c) + 2} \cdot \frac{c^{2} + 3 c + 2}{c - 1}$

Step 1.2

Factor $2$ out of $2$ .

$\frac{4 c}{2 (c) + 2 (1)} \cdot \frac{c^{2} + 3 c + 2}{c - 1}$

Step 1.3

Factor $2$ out of $2 (c) + 2 (1)$ .

$\frac{4 c}{2 (c + 1)} \cdot \frac{c^{2} + 3 c + 2}{c - 1}$

Step 2

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

$1, 2$

Step 2.2

Write the factored form using these integers.

$\frac{4 c}{2 (c + 1)} \cdot \frac{(c + 1) (c + 2)}{c - 1}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $c + 1$ .

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Step 3.1.1

Factor $c + 1$ out of $2 (c + 1)$ .

$\frac{4 c}{(c + 1) \cdot 2} \cdot \frac{(c + 1) (c + 2)}{c - 1}$

Step 3.1.2

Cancel the common factor.

$\frac{4 c}{(c + 1) \cdot 2} \cdot \frac{(c + 1) (c + 2)}{c - 1}$

Step 3.1.3

Rewrite the expression.

$\frac{4 c}{2} \cdot \frac{c + 2}{c - 1}$

Step 3.2

Multiply $\frac{4 c}{2}$ by $\frac{c + 2}{c - 1}$ .

$\frac{4 c (c + 2)}{2 (c - 1)}$

Step 3.3

Cancel the common factor of $4$ and $2$ .

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Step 3.3.1

Factor $2$ out of $4 c (c + 2)$ .

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

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Cancel the common factor.

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

Step 3.3.2.2

Rewrite the expression.

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