Calculus Examples

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

Step 1

Simplify the denominator.

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Step 1.1

Cancel the common factor of $2$ .

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Step 1.1.1

Factor $2$ out of $- 2$ .

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

Step 1.1.2

Factor $2$ out of $4$ .

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

Step 1.1.3

Cancel the common factor.

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

Step 1.1.4

Rewrite the expression.

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

Step 1.2

Rewrite $- 1 (\frac{1}{2})$ as $- (\frac{1}{2})$ .

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

Step 1.3

Write $1$ as a fraction with a common denominator.

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Add $- 1$ and $2$ .

$\frac{2}{{(\frac{1}{2})}^{2}}$

Step 1.6

Apply the product rule to $\frac{1}{2}$ .

$\frac{2}{\frac{1^{2}}{2^{2}}}$

Step 1.7

One to any power is one.

$\frac{2}{\frac{1}{2^{2}}}$

Step 1.8

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

$\frac{2}{\frac{1}{4}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$2 \cdot 4$

Step 3

Multiply $2$ by $4$ .

$8$