Linear Algebra Examples

$\frac{\frac{x}{12} \cdot \frac{1}{4}}{\frac{1}{4} x} + \frac{5}{12}$

Step 1

Set the denominator in $\frac{\frac{x}{12} \cdot \frac{1}{4}}{\frac{1}{4} x}$ equal to $0$ to find where the expression is undefined.

$\frac{1}{4} x = 0$

Step 2

Solve for $x$ .

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Step 2.1

Multiply both sides of the equation by $4$ .

$4 (\frac{1}{4} x) = 4 \cdot 0$

Step 2.2

Simplify both sides of the equation.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Simplify $4 (\frac{1}{4} x)$ .

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Step 2.2.1.1.1

Combine $\frac{1}{4}$ and $x$ .

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

Step 2.2.1.1.2

Cancel the common factor of $4$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

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

Step 2.2.1.1.2.2

Rewrite the expression.

$x = 4 \cdot 0$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Multiply $4$ by $0$ .

$x = 0$

Step 3

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

Interval Notation:

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

Set-Builder Notation:

${x | x \neq 0}$

Step 4