Algebra Examples

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

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

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

Step 1.2

Combine exponents.

Tap for more steps...

Step 1.2.1

Rewrite $\frac{1}{2}$ as $2^{- 1}$ .

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

Step 1.2.2

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

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

Step 1.2.3

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 1.2.4

Multiply $- 1$ by $1$ .

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

Step 1.2.5

Multiply the exponents in ${(2^{- 1})}^{2}$ .

Tap for more steps...

Step 1.2.5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 1.2.5.2

Multiply $- 1$ by $2$ .

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

Step 1.2.6

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.2.7

Add $- 2$ and $1$ .

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

Step 1.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 1.4

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

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

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.2

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

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

Step 2.3

Multiply $\frac{1^{2}}{2^{2}}$ by $1$ .

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

Step 2.4

One to any power is one.

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

Step 2.5

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

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

Step 2.6

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 2.7

Combine $- 1$ and $\frac{4}{4}$ .

$\frac{\frac{1}{2} \cdot 1}{\frac{1}{4} + \frac{- 1 \cdot 4}{4}}$

Step 2.8

Combine the numerators over the common denominator.

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

Step 2.9

Simplify the numerator.

Tap for more steps...

Step 2.9.1

Multiply $- 1$ by $4$ .

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

Step 2.9.2

Subtract $4$ from $1$ .

$\frac{\frac{1}{2} \cdot 1}{\frac{- 3}{4}}$

Step 2.10

Move the negative in front of the fraction.

$\frac{\frac{1}{2} \cdot 1}{- \frac{3}{4}}$

Step 3

Multiply $\frac{1}{2}$ by $1$ .

$\frac{\frac{1}{2}}{- \frac{3}{4}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} (- \frac{4}{3})$

Step 5

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{1}{2} \cdot \frac{- 4}{3}$

Step 5.2

Factor $2$ out of $- 4$ .

$\frac{1}{2} \cdot \frac{2 (- 2)}{3}$

Step 5.3

Cancel the common factor.

$\frac{1}{2} \cdot \frac{2 \cdot - 2}{3}$

Step 5.4

Rewrite the expression.

$\frac{- 2}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{2}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{3}$

Decimal Form:

$- 0.\overline{6}$