Basic Math Examples

$\frac{2 a - 1}{a - 3} \cdot \frac{1}{a^{2} - a - 6}$

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.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Raise $a - 3$ to the power of $1$ .

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

Step 2.3

Raise $a - 3$ to the power of $1$ .

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

Step 2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.5

Add $1$ and $1$ .

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