Precalculus Examples

$f (x) = x^{2} - x - 6$ ; calcula $\frac{f (- 5)}{f (2)}$

Step 1

Evaluate the numerator in $\frac{f (- 5)}{f (2)}$ .

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Step 1.1

Replace the variable $x$ with $- 5$ in the expression.

$f (- 5) = {(- 5)}^{2} - (- 5) - 6$

Step 1.2

Simplify ${(- 5)}^{2} - (- 5) - 6$ .

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Step 1.2.1

Remove parentheses.

${(- 5)}^{2} - (- 5) - 6$

Step 1.2.2

Simplify each term.

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Step 1.2.2.1

Raise $- 5$ to the power of $2$ .

$25 - (- 5) - 6$

Step 1.2.2.2

Multiply $- 1$ by $- 5$ .

$25 + 5 - 6$

Step 1.2.3

Simplify by adding and subtracting.

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Step 1.2.3.1

Add $25$ and $5$ .

$30 - 6$

Step 1.2.3.2

Subtract $6$ from $30$ .

$24$

Step 2

Evaluate the denominator in $\frac{f (- 5)}{f (2)}$ .

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Step 2.1

Replace the variable $x$ with $2$ in the expression.

$f (2) = {(2)}^{2} - (2) - 6$

Step 2.2

Simplify ${(2)}^{2} - (2) - 6$ .

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Step 2.2.1

Remove parentheses.

${(2)}^{2} - (2) - 6$

Step 2.2.2

Simplify each term.

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Step 2.2.2.1

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

$4 - (2) - 6$

Step 2.2.2.2

Multiply $- 1$ by $2$ .

$4 - 2 - 6$

Step 2.2.3

Simplify by subtracting numbers.

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Step 2.2.3.1

Subtract $2$ from $4$ .

$2 - 6$

Step 2.2.3.2

Subtract $6$ from $2$ .

$- 4$

Step 3

Rewrite $\frac{f (- 5)}{f (2)}$ .

$\frac{24}{- 4}$

Step 4

Divide $24$ by $- 4$ .

$- 6$