Calculus Examples

$- \frac{4 {(- 1)}^{2} - 16 \cdot - 1}{{(4 (- 1) + 8)}^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $- 1$ to the power of $2$ .

$- \frac{4 \cdot 1 - 16 \cdot - 1}{{(4 (- 1) + 8)}^{2}}$

Step 1.2

Multiply $4$ by $1$ .

$- \frac{4 - 16 \cdot - 1}{{(4 (- 1) + 8)}^{2}}$

Step 1.3

Multiply $- 16$ by $- 1$ .

$- \frac{4 + 16}{{(4 (- 1) + 8)}^{2}}$

Step 1.4

Add $4$ and $16$ .

$- \frac{20}{{(4 (- 1) + 8)}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $4$ by $- 1$ .

$- \frac{20}{{(- 4 + 8)}^{2}}$

Step 2.2

Add $- 4$ and $8$ .

$- \frac{20}{4^{2}}$

Step 2.3

Raise $4$ to the power of $2$ .

$- \frac{20}{16}$

Step 3

Cancel the common factor of $20$ and $16$ .

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Step 3.1

Factor $4$ out of $20$ .

$- \frac{4 (5)}{16}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $16$ .

$- \frac{4 \cdot 5}{4 \cdot 4}$

Step 3.2.2

Cancel the common factor.

$- \frac{4 \cdot 5}{4 \cdot 4}$

Step 3.2.3

Rewrite the expression.

$- \frac{5}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{4}$

Decimal Form:

$- 1.25$

Mixed Number Form:

$- 1 \frac{1}{4}$