Precalculus Examples

$f (- 7) = \frac{x^{2} + x - 6}{x^{2} + 3 x - 10}$

Step 1

Replace the variable $x$ with $- 7$ in the expression.

$f (- 7) = \frac{{(- 7)}^{2} - 7 - 6}{{(- 7)}^{2} + 3 (- 7) - 10}$

Step 2

Simplify the result.

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Step 2.1

Remove parentheses.

$f (- 7) = \frac{{(- 7)}^{2} - 7 - 6}{{(- 7)}^{2} + 3 (- 7) - 10}$

Step 2.2

Simplify the numerator.

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Step 2.2.1

Raise $- 7$ to the power of $2$ .

$f (- 7) = \frac{49 - 7 - 6}{{(- 7)}^{2} + 3 (- 7) - 10}$

Step 2.2.2

Subtract $7$ from $49$ .

$f (- 7) = \frac{42 - 6}{{(- 7)}^{2} + 3 (- 7) - 10}$

Step 2.2.3

Subtract $6$ from $42$ .

$f (- 7) = \frac{36}{{(- 7)}^{2} + 3 (- 7) - 10}$

Step 2.3

Simplify the denominator.

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Step 2.3.1

Raise $- 7$ to the power of $2$ .

$f (- 7) = \frac{36}{49 + 3 (- 7) - 10}$

Step 2.3.2

Multiply $3$ by $- 7$ .

$f (- 7) = \frac{36}{49 - 21 - 10}$

Step 2.3.3

Subtract $21$ from $49$ .

$f (- 7) = \frac{36}{28 - 10}$

Step 2.3.4

Subtract $10$ from $28$ .

$f (- 7) = \frac{36}{18}$

Step 2.4

Divide $36$ by $18$ .

$f (- 7) = 2$

Step 2.5

The final answer is $2$ .

$2$

Step 3