Precalculus Examples

$\frac{2 (a - b)}{a (a + b)}$

Step 1

Set the denominator in $\frac{2 (a - b)}{a (a + b)}$ equal to $0$ to find where the expression is undefined.

$a (a + b) = 0$

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 $0$ .

$a = 0$

$a + b = 0$

Step 2.2

Set $a$ equal to $0$ .

$a = 0$

Step 2.3

Set $a + b$ equal to $0$ and solve for $a$ .

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Step 2.3.1

Set $a + b$ equal to $0$ .

$a + b = 0$

Step 2.3.2

Subtract $b$ from both sides of the equation.

$a = - b$

Step 2.4

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

$a = 0$

$a = - b$

$a = 0$

$a = - b$

Step 3

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

Interval Notation:

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

Set-Builder Notation:

${a | a \neq 0}$