Precalculus Examples

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

Step 1

Set the denominator in $\frac{3 (2 a - b)}{a (2 a + b)}$ equal to $0$ to find where the expression is undefined.

$a (2 a + b) = 0$

Step 2

Solve for $a$ .

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Step 2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$a = 0$

$2 a + b = 0$

Step 2.2

Set $a$ equal to $0$ .

$a = 0$

Step 2.3

Set $2 a + b$ equal to $0$ and solve for $a$ .

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Step 2.3.1

Set $2 a + b$ equal to $0$ .

$2 a + b = 0$

Step 2.3.2

Solve $2 a + b = 0$ for $a$ .

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Step 2.3.2.1

Subtract $b$ from both sides of the equation.

$2 a = - b$

Step 2.3.2.2

Divide each term in $2 a = - b$ by $2$ and simplify.

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Step 2.3.2.2.1

Divide each term in $2 a = - b$ by $2$ .

$\frac{2 a}{2} = \frac{- b}{2}$

Step 2.3.2.2.2

Simplify the left side.

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Step 2.3.2.2.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.2.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{- b}{2}$

Step 2.3.2.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{- b}{2}$

Step 2.3.2.2.3

Simplify the right side.

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Step 2.3.2.2.3.1

Move the negative in front of the fraction.

$a = - \frac{b}{2}$

Step 2.4

The final solution is all the values that make $a (2 a + b) = 0$ true.

$a = 0$

$a = - \frac{b}{2}$

$a = 0$

$a = - \frac{b}{2}$

Step 3

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

Interval Notation:

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

Set-Builder Notation:

${a | a \neq 0}$