Precalculus Examples

$\frac{a + 1}{a (a - 1)}$

Step 1

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

$a (a - 1) = 0$

Step 2

Solve for $a$ .

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Step 2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$a = 0$

$a - 1 = 0$

Step 2.2

Set $a$ equal to $0$ .

$a = 0$

Step 2.3

Set $a - 1$ equal to $0$ and solve for $a$ .

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Step 2.3.1

Set $a - 1$ equal to $0$ .

$a - 1 = 0$

Step 2.3.2

Add $1$ to both sides of the equation.

$a = 1$

Step 2.4

The final solution is all the values that make $a (a - 1) = 0$ true.

$a = 0, 1$

Step 3

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

Interval Notation:

$(- \infty, 0) \cup (0, 1) \cup (1, \infty)$

Set-Builder Notation:

${a | a \neq 0, 1}$

Step 4