Precalculus Examples

$g (x) = x^{2} - \frac{4}{4 x} \cdot g (n - 3)$

Step 1

Set the denominator in $\frac{4}{4 x}$ equal to $0$ to find where the expression is undefined.

$4 x = 0$

Step 2

Divide each term in $4 x = 0$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 x = 0$ by $4$ .

$\frac{4 x}{4} = \frac{0}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{0}{4}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $4$ .

$x = 0$

Step 3

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

Interval Notation:

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

Set-Builder Notation:

${x | x \neq 0}$