Precalculus Examples

$f (- 3) = \frac{4 x - 8}{x^{2} - 3 x - 4}$

Step 1

Replace the variable $x$ with $- 3$ in the expression.

$f (- 3) = \frac{4 (- 3) - 8}{{(- 3)}^{2} - 3 \cdot - 3 - 4}$

Step 2

Simplify the result.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Multiply $4$ by $- 3$ .

$f (- 3) = \frac{- 12 - 8}{{(- 3)}^{2} - 3 \cdot - 3 - 4}$

Step 2.1.2

Subtract $8$ from $- 12$ .

$f (- 3) = \frac{- 20}{{(- 3)}^{2} - 3 \cdot - 3 - 4}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Raise $- 3$ to the power of $2$ .

$f (- 3) = \frac{- 20}{9 - 3 \cdot - 3 - 4}$

Step 2.2.2

Multiply $- 3$ by $- 3$ .

$f (- 3) = \frac{- 20}{9 + 9 - 4}$

Step 2.2.3

Add $9$ and $9$ .

$f (- 3) = \frac{- 20}{18 - 4}$

Step 2.2.4

Subtract $4$ from $18$ .

$f (- 3) = \frac{- 20}{14}$

Step 2.3

Reduce the expression by cancelling the common factors.

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Step 2.3.1

Cancel the common factor of $- 20$ and $14$ .

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Step 2.3.1.1

Factor $2$ out of $- 20$ .

$f (- 3) = \frac{2 (- 10)}{14}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $2$ out of $14$ .

$f (- 3) = \frac{2 \cdot - 10}{2 \cdot 7}$

Step 2.3.1.2.2

Cancel the common factor.

$f (- 3) = \frac{2 \cdot - 10}{2 \cdot 7}$

Step 2.3.1.2.3

Rewrite the expression.

$f (- 3) = \frac{- 10}{7}$

Step 2.3.2

Move the negative in front of the fraction.

$f (- 3) = - \frac{10}{7}$

Step 2.4

The final answer is $- \frac{10}{7}$ .

$- \frac{10}{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{10}{7}$

Decimal Form:

$- 1.\overline{428571}$

Mixed Number Form:

$- 1 \frac{3}{7}$

Step 4