Basic Math Examples

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

Step 1

Factor $4$ out of $4 a + 4$ .

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Step 1.1

Factor $4$ out of $4 a$ .

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

Step 1.2

Factor $4$ out of $4$ .

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

Step 1.3

Factor $4$ out of $4 (a) + 4 (1)$ .

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

Step 2

Factor $a^{2} - a - 2$ 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 $- 1$ .

$- 2, 1$

Step 2.2

Write the factored form using these integers.

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $a + 1$ .

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Step 3.1.1

Factor $a + 1$ out of $4 (a + 1)$ .

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

Step 3.1.2

Factor $a + 1$ out of $(a - 2) (a + 1)$ .

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

Step 3.1.3

Cancel the common factor.

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

Step 3.1.4

Rewrite the expression.

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

Step 3.2

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

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