Basic Math Examples

$\frac{a^{2} - a - 6}{a^{2} + 3 a + 2}$

Step 1

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

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Step 1.1

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 1.2

Write the factored form using these integers.

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

Step 2

Factor $a^{2} + 3 a + 2$ 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 $3$ .

$1, 2$

Step 2.2

Write the factored form using these integers.

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

Step 3

Cancel the common factor of $a + 2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{a - 3}{a + 1}$