Precalculus Examples

$- \frac{25 x^{3} y^{3}}{14 a^{2} b} \cdot (- \frac{21 a b}{10 x^{2} y})$

Step 1

Set the denominator in $\frac{25 x^{3} y^{3}}{14 a^{2} b}$ equal to $0$ to find where the expression is undefined.

$14 a^{2} b = 0$

Step 2

Solve for $x$ .

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Step 2.1

Divide each term in $14 a^{2} b = 0$ by $14 b$ and simplify.

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Step 2.1.1

Divide each term in $14 a^{2} b = 0$ by $14 b$ .

$\frac{14 a^{2} b}{14 b} = \frac{0}{14 b}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $14$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{14 a^{2} b}{14 b} = \frac{0}{14 b}$

Step 2.1.2.1.2

Rewrite the expression.

$\frac{a^{2} b}{b} = \frac{0}{14 b}$

Step 2.1.2.2

Cancel the common factor of $b$ .

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Step 2.1.2.2.1

Cancel the common factor.

$\frac{a^{2} b}{b} = \frac{0}{14 b}$

Step 2.1.2.2.2

Divide $a^{2}$ by $1$ .

$a^{2} = \frac{0}{14 b}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Cancel the common factor of $0$ and $14$ .

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Step 2.1.3.1.1

Factor $14$ out of $0$ .

$a^{2} = \frac{14 (0)}{14 b}$

Step 2.1.3.1.2

Cancel the common factors.

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Step 2.1.3.1.2.1

Factor $14$ out of $14 b$ .

$a^{2} = \frac{14 (0)}{14 (b)}$

Step 2.1.3.1.2.2

Cancel the common factor.

$a^{2} = \frac{14 \cdot 0}{14 b}$

Step 2.1.3.1.2.3

Rewrite the expression.

$a^{2} = \frac{0}{b}$

Step 2.1.3.2

Divide $0$ by $b$ .

$a^{2} = 0$

Step 2.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$a = \pm \sqrt{0}$

Step 2.3

Simplify $\pm \sqrt{0}$ .

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Step 2.3.1

Rewrite $0$ as $0^{2}$ .

$a = \pm \sqrt{0^{2}}$

Step 2.3.2

Pull terms out from under the radical, assuming positive real numbers.

$a = \pm 0$

Step 2.3.3

Plus or minus $0$ is $0$ .

$a = 0$

Step 3

Set the denominator in $\frac{21 a b}{10 x^{2} y}$ equal to $0$ to find where the expression is undefined.

$10 x^{2} y = 0$

Step 4

Solve for $x$ .

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Step 4.1

Divide each term in $10 x^{2} y = 0$ by $10 y$ and simplify.

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Step 4.1.1

Divide each term in $10 x^{2} y = 0$ by $10 y$ .

$\frac{10 x^{2} y}{10 y} = \frac{0}{10 y}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $10$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{10 x^{2} y}{10 y} = \frac{0}{10 y}$

Step 4.1.2.1.2

Rewrite the expression.

$\frac{x^{2} y}{y} = \frac{0}{10 y}$

Step 4.1.2.2

Cancel the common factor of $y$ .

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Step 4.1.2.2.1

Cancel the common factor.

$\frac{x^{2} y}{y} = \frac{0}{10 y}$

Step 4.1.2.2.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{0}{10 y}$

Step 4.1.3

Simplify the right side.

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Step 4.1.3.1

Cancel the common factor of $0$ and $10$ .

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Step 4.1.3.1.1

Factor $10$ out of $0$ .

$x^{2} = \frac{10 (0)}{10 y}$

Step 4.1.3.1.2

Cancel the common factors.

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Step 4.1.3.1.2.1

Factor $10$ out of $10 y$ .

$x^{2} = \frac{10 (0)}{10 (y)}$

Step 4.1.3.1.2.2

Cancel the common factor.

$x^{2} = \frac{10 \cdot 0}{10 y}$

Step 4.1.3.1.2.3

Rewrite the expression.

$x^{2} = \frac{0}{y}$

Step 4.1.3.2

Divide $0$ by $y$ .

$x^{2} = 0$

Step 4.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Step 4.3

Simplify $\pm \sqrt{0}$ .

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Step 4.3.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 4.3.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Step 4.3.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 5

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

Interval Notation:

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

Set-Builder Notation:

${x | x \neq 0}$