Precalculus Examples

${(\frac{2 a + 3 b}{2 a} + \frac{2 a - 3 b}{3 b})}^{2} - {(\frac{2 a + 3 b}{2 a} - \frac{2 a - 3 b}{3 b})}^{2}$

Step 1

Set the denominator in $\frac{2 a + 3 b}{2 a}$ equal to $0$ to find where the expression is undefined.

$2 a = 0$

Step 2

Divide each term in $2 a = 0$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 a = 0$ by $2$ .

$\frac{2 a}{2} = \frac{0}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{0}{2}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a = \frac{0}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $2$ .

$a = 0$

Step 3

Set the denominator in $\frac{2 a - 3 b}{3 b}$ equal to $0$ to find where the expression is undefined.

$3 b = 0$

Step 4

Divide each term in $3 b = 0$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 b = 0$ by $3$ .

$\frac{3 b}{3} = \frac{0}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 b}{3} = \frac{0}{3}$

Step 4.2.1.2

Divide $b$ by $1$ .

$b = \frac{0}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $3$ .

$b = 0$

Step 5

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

Interval Notation:

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

Set-Builder Notation:

${a | a \neq 0}$