Linear Algebra Examples

$\frac{1}{6 k^{2}} = \frac{1}{3 k^{2}} - \frac{1}{k}$

Step 1

Set the denominator in $\frac{1}{6 k^{2}}$ equal to $0$ to find where the expression is undefined.

$6 k^{2} = 0$

Step 2

Solve for $k$ .

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Step 2.1

Divide each term in $6 k^{2} = 0$ by $6$ and simplify.

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Step 2.1.1

Divide each term in $6 k^{2} = 0$ by $6$ .

$\frac{6 k^{2}}{6} = \frac{0}{6}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $6$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{6 k^{2}}{6} = \frac{0}{6}$

Step 2.1.2.1.2

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

$k^{2} = \frac{0}{6}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Divide $0$ by $6$ .

$k^{2} = 0$

Step 2.2

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

$k = \pm \sqrt{0}$

Step 2.3

Simplify $\pm \sqrt{0}$ .

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Step 2.3.1

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

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

Step 2.3.2

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

$k = \pm 0$

Step 2.3.3

Plus or minus $0$ is $0$ .

$k = 0$

Step 3

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

Interval Notation:

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

Set-Builder Notation:

${k | k \neq 0}$

Step 4