Precalculus Examples

$\frac{2 m^{2}}{n^{2}}$

Step 1

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

$n^{2} = 0$

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.

$n = \pm \sqrt{0}$

Step 2.2

Simplify $\pm \sqrt{0}$ .

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Step 2.2.1

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

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

Step 2.2.2

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

$n = \pm 0$

Step 2.2.3

Plus or minus $0$ is $0$ .

$n = 0$

Step 3

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

Interval Notation:

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

Set-Builder Notation:

${m | m \neq 0}$