Precalculus Examples

$- \frac{10 a^{2} x}{9 b y}$

Step 1

Set the denominator in $\frac{10 a^{2} x}{9 b y}$ equal to $0$ to find where the expression is undefined.

$9 b y = 0$

Step 2

Divide each term in $9 b y = 0$ by $9 y$ and simplify.

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Step 2.1

Divide each term in $9 b y = 0$ by $9 y$ .

$\frac{9 b y}{9 y} = \frac{0}{9 y}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $9$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{9 b y}{9 y} = \frac{0}{9 y}$

Step 2.2.1.2

Rewrite the expression.

$\frac{b y}{y} = \frac{0}{9 y}$

Step 2.2.2

Cancel the common factor of $y$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{b y}{y} = \frac{0}{9 y}$

Step 2.2.2.2

Divide $b$ by $1$ .

$b = \frac{0}{9 y}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $0$ and $9$ .

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Step 2.3.1.1

Factor $9$ out of $0$ .

$b = \frac{9 (0)}{9 y}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $9$ out of $9 y$ .

$b = \frac{9 (0)}{9 (y)}$

Step 2.3.1.2.2

Cancel the common factor.

$b = \frac{9 \cdot 0}{9 y}$

Step 2.3.1.2.3

Rewrite the expression.

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

Step 2.3.2

Divide $0$ by $y$ .

$b = 0$

Step 3

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

Interval Notation:

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

Set-Builder Notation:

${a | a \neq 0}$