Precalculus Examples

$\frac{a b^{2} - a^{2} b}{a b} \cdot \frac{a^{2} b^{2}}{a - b}$

Step 1

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

$a b = 0$

Step 2

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

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $b$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $a$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $b$ .

$a = 0$

Step 3

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

$a - b = 0$

Step 4

Add $b$ to both sides of the equation.

$a = b$

Step 5

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

Interval Notation:

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

Set-Builder Notation:

${a | a \neq 0}$