Trigonometry Examples

$\frac{{(2 m^{2})}^{- 1}}{m^{2}}$

Step 1

Set the denominator in $\frac{{(2 m^{2})}^{- 1}}{m^{2}}$ equal to $0$ to find where the expression is undefined.

$m^{2} = 0$

Step 2

Solve for $m$ .

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Step 2.1

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

$m = \pm \sqrt{0}$

Step 2.2

Simplify $\pm \sqrt{0}$ .

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Step 2.2.1

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

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

Step 2.2.2

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

$m = \pm 0$

Step 2.2.3

Plus or minus $0$ is $0$ .

$m = 0$

Step 3

Set the base in ${(2 m^{2})}^{- 1}$ equal to $0$ to find where the expression is undefined.

$2 m^{2} = 0$

Step 4

Solve for $m$ .

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Step 4.1

Divide each term in $2 m^{2} = 0$ by $2$ and simplify.

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Step 4.1.1

Divide each term in $2 m^{2} = 0$ by $2$ .

$\frac{2 m^{2}}{2} = \frac{0}{2}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $2$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{2 m^{2}}{2} = \frac{0}{2}$

Step 4.1.2.1.2

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

$m^{2} = \frac{0}{2}$

Step 4.1.3

Simplify the right side.

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Step 4.1.3.1

Divide $0$ by $2$ .

$m^{2} = 0$

Step 4.2

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

$m = \pm \sqrt{0}$

Step 4.3

Simplify $\pm \sqrt{0}$ .

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Step 4.3.1

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

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

Step 4.3.2

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

$m = \pm 0$

Step 4.3.3

Plus or minus $0$ is $0$ .

$m = 0$

Step 5

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

Interval Notation:

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

Set-Builder Notation:

${m | m \neq 0}$

Step 6