Precalculus Examples

$- \frac{c - b}{a (3 a - c)}$

Step 1

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

$a (3 a - c) = 0$

Step 2

Solve for $c$ .

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Step 2.1

Divide each term in $a (3 a - c) = 0$ by $a$ and simplify.

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Step 2.1.1

Divide each term in $a (3 a - c) = 0$ by $a$ .

$\frac{a (3 a - c)}{a} = \frac{0}{a}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $a$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{a (3 a - c)}{a} = \frac{0}{a}$

Step 2.1.2.1.2

Divide $3 a - c$ by $1$ .

$3 a - c = \frac{0}{a}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Divide $0$ by $a$ .

$3 a - c = 0$

Step 2.2

Subtract $3 a$ from both sides of the equation.

$- c = - 3 a$

Step 2.3

Divide each term in $- c = - 3 a$ by $- 1$ and simplify.

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Step 2.3.1

Divide each term in $- c = - 3 a$ by $- 1$ .

$\frac{- c}{- 1} = \frac{- 3 a}{- 1}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Dividing two negative values results in a positive value.

$\frac{c}{1} = \frac{- 3 a}{- 1}$

Step 2.3.2.2

Divide $c$ by $1$ .

$c = \frac{- 3 a}{- 1}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Move the negative one from the denominator of $\frac{- 3 a}{- 1}$ .

$c = - 1 \cdot (- 3 a)$

Step 2.3.3.2

Rewrite $- 1 \cdot (- 3 a)$ as $- (- 3 a)$ .

$c = - (- 3 a)$

Step 2.3.3.3

Multiply $- 3$ by $- 1$ .

$c = 3 a$

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${c | c \in ℝ}$