Precalculus Examples

$\frac{a - 4}{4 a - 8} + \frac{1}{2 a - 4}$

Step 1

Set the denominator in $\frac{a - 4}{4 a - 8}$ equal to $0$ to find where the expression is undefined.

$4 a - 8 = 0$

Step 2

Solve for $a$ .

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Step 2.1

Add $8$ to both sides of the equation.

$4 a = 8$

Step 2.2

Divide each term in $4 a = 8$ by $4$ and simplify.

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Step 2.2.1

Divide each term in $4 a = 8$ by $4$ .

$\frac{4 a}{4} = \frac{8}{4}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $4$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{4 a}{4} = \frac{8}{4}$

Step 2.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{8}{4}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $8$ by $4$ .

$a = 2$

Step 3

Set the denominator in $\frac{1}{2 a - 4}$ equal to $0$ to find where the expression is undefined.

$2 a - 4 = 0$

Step 4

Solve for $a$ .

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Step 4.1

Add $4$ to both sides of the equation.

$2 a = 4$

Step 4.2

Divide each term in $2 a = 4$ by $2$ and simplify.

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Step 4.2.1

Divide each term in $2 a = 4$ by $2$ .

$\frac{2 a}{2} = \frac{4}{2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{4}{2}$

Step 4.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{4}{2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $4$ by $2$ .

$a = 2$

Step 5

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

Interval Notation:

$(- \infty, 2) \cup (2, \infty)$

Set-Builder Notation:

${a | a \neq 2}$

Step 6