Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

One to any power is one.

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

Step 1.3

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

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

One to any power is one.

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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

$\frac{3 (\frac{1}{4})}{\frac{1}{4} + \frac{- 1 \cdot 4}{4}}$

Step 2.6

Combine the numerators over the common denominator.

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

Step 2.7

Simplify the numerator.

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Step 2.7.1

Multiply $- 1$ by $4$ .

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

Step 2.7.2

Subtract $4$ from $1$ .

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

Step 2.8

Move the negative in front of the fraction.

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

Step 3

Simplify terms.

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Step 3.1

Combine $3$ and $\frac{1}{4}$ .

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

Step 3.2

Cancel the common factor of $\frac{3}{4}$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

$\frac{1}{- 1}$

Step 3.2.3

Move the negative one from the denominator of $\frac{1}{- 1}$ .

$- 1 \cdot 1$

Step 3.3

Multiply $- 1$ by $1$ .

$- 1$