Finite Math Examples

$\frac{2 a}{51 x^{6} y} \cdot (17 x^{7} y)$

Step 1

Set the denominator in $\frac{2 a}{51 x^{6} y}$ equal to $0$ to find where the expression is undefined.

$51 x^{6} y = 0$

Step 2

Solve for $a$ .

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Step 2.1

Divide each term in $51 x^{6} y = 0$ by $51 y$ and simplify.

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Step 2.1.1

Divide each term in $51 x^{6} y = 0$ by $51 y$ .

$\frac{51 x^{6} y}{51 y} = \frac{0}{51 y}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $51$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{51 x^{6} y}{51 y} = \frac{0}{51 y}$

Step 2.1.2.1.2

Rewrite the expression.

$\frac{x^{6} y}{y} = \frac{0}{51 y}$

Step 2.1.2.2

Cancel the common factor of $y$ .

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Step 2.1.2.2.1

Cancel the common factor.

$\frac{x^{6} y}{y} = \frac{0}{51 y}$

Step 2.1.2.2.2

Divide $x^{6}$ by $1$ .

$x^{6} = \frac{0}{51 y}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Cancel the common factor of $0$ and $51$ .

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Step 2.1.3.1.1

Factor $51$ out of $0$ .

$x^{6} = \frac{51 (0)}{51 y}$

Step 2.1.3.1.2

Cancel the common factors.

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Step 2.1.3.1.2.1

Factor $51$ out of $51 y$ .

$x^{6} = \frac{51 (0)}{51 (y)}$

Step 2.1.3.1.2.2

Cancel the common factor.

$x^{6} = \frac{51 \cdot 0}{51 y}$

Step 2.1.3.1.2.3

Rewrite the expression.

$x^{6} = \frac{0}{y}$

Step 2.1.3.2

Divide $0$ by $y$ .

$x^{6} = 0$

Step 2.2

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

$x = \pm \sqrt[6]{0}$

Step 2.3

Simplify $\pm \sqrt[6]{0}$ .

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Step 2.3.1

Rewrite $0$ as $0^{6}$ .

$x = \pm \sqrt[6]{0^{6}}$

Step 2.3.2

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

$x = \pm 0$

Step 2.3.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 3

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

Interval Notation:

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

Set-Builder Notation:

${a | a \neq 0}$