Precalculus Examples

$\frac{k x + k^{2}}{x^{2}} \cdot \frac{x}{x + k}$

Step 1

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

$x^{2} = 0$

Step 2

Solve for $k$ .

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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.

$x = \pm \sqrt{0}$

Step 2.2

Simplify $\pm \sqrt{0}$ .

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Step 2.2.1

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

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

Step 2.2.2

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

$x = \pm 0$

Step 2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 3

Set the denominator in $\frac{x}{x + k}$ equal to $0$ to find where the expression is undefined.

$x + k = 0$

Step 4

Subtract $x$ from both sides of the equation.

$k = - x$

Step 5

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

Interval Notation:

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

Set-Builder Notation:

${k | k \neq 0}$