Precalculus Examples

$h (x) = \frac{4}{\frac{3}{x} - 1}$

Step 1

Set the denominator in $\frac{3}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 2

Set the denominator in $\frac{4}{\frac{3}{x} - 1}$ equal to $0$ to find where the expression is undefined.

$\frac{3}{x} - 1 = 0$

Step 3

Solve for $x$ .

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Step 3.1

Add $1$ to both sides of the equation.

$\frac{3}{x} = 1$

Step 3.2

Find the LCD of the terms in the equation.

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Step 3.2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x, 1$

Step 3.2.2

The LCM of one and any expression is the expression.

$x$

Step 3.3

Multiply each term in $\frac{3}{x} = 1$ by $x$ to eliminate the fractions.

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Step 3.3.1

Multiply each term in $\frac{3}{x} = 1$ by $x$ .

$\frac{3}{x} x = 1 x$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $x$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{3}{x} x = 1 x$

Step 3.3.2.1.2

Rewrite the expression.

$3 = 1 x$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Multiply $x$ by $1$ .

$3 = x$

Step 3.4

Rewrite the equation as $x = 3$ .

$x = 3$

Step 4

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

Interval Notation:

$(- \infty, 0) \cup (0, 3) \cup (3, \infty)$

Set-Builder Notation:

${x | x \neq 0, 3}$

Step 5