Precalculus Examples

$\frac{3 a + 12 b}{6 a b}$

Step 1

Set the denominator in $\frac{3 a + 12 b}{6 a b}$ equal to $0$ to find where the expression is undefined.

$6 a b = 0$

Step 2

Divide each term in $6 a b = 0$ by $6 b$ and simplify.

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Step 2.1

Divide each term in $6 a b = 0$ by $6 b$ .

$\frac{6 a b}{6 b} = \frac{0}{6 b}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 a b}{6 b} = \frac{0}{6 b}$

Step 2.2.1.2

Rewrite the expression.

$\frac{a b}{b} = \frac{0}{6 b}$

Step 2.2.2

Cancel the common factor of $b$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{a b}{b} = \frac{0}{6 b}$

Step 2.2.2.2

Divide $a$ by $1$ .

$a = \frac{0}{6 b}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $0$ and $6$ .

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Step 2.3.1.1

Factor $6$ out of $0$ .

$a = \frac{6 (0)}{6 b}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $6$ out of $6 b$ .

$a = \frac{6 (0)}{6 (b)}$

Step 2.3.1.2.2

Cancel the common factor.

$a = \frac{6 \cdot 0}{6 b}$

Step 2.3.1.2.3

Rewrite the expression.

$a = \frac{0}{b}$

Step 2.3.2

Divide $0$ by $b$ .

$a = 0$

Step 3

The domain is all values of $a$ that make the expression defined.

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${a | a \neq 0}$