Algebra Examples

$\frac{6 {(- \frac{1}{2})}^{2}}{{(- \frac{1}{2})}^{2} - 4}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{6 {(- 1)}^{2} {(\frac{1}{2})}^{2}}{{(- \frac{1}{2})}^{2} - 4}$

Step 1.2

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

$\frac{6 \cdot 1 {(\frac{1}{2})}^{2}}{{(- \frac{1}{2})}^{2} - 4}$

Step 1.3

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

$\frac{6 \cdot 1 \frac{1^{2}}{2^{2}}}{{(- \frac{1}{2})}^{2} - 4}$

Step 1.4

One to any power is one.

$\frac{6 \cdot 1 \frac{1}{2^{2}}}{{(- \frac{1}{2})}^{2} - 4}$

Step 1.5

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

$\frac{6 \cdot 1 \frac{1}{4}}{{(- \frac{1}{2})}^{2} - 4}$

Step 1.6

Combine exponents.

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Step 1.6.1

Multiply $6$ by $1$ .

$\frac{6 (\frac{1}{4})}{{(- \frac{1}{2})}^{2} - 4}$

Step 1.6.2

Combine $6$ and $\frac{1}{4}$ .

$\frac{\frac{6}{4}}{{(- \frac{1}{2})}^{2} - 4}$

Step 1.7

Cancel the common factor of $6$ and $4$ .

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Step 1.7.1

Factor $2$ out of $6$ .

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

Step 1.7.2

Cancel the common factors.

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Step 1.7.2.1

Factor $2$ out of $4$ .

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

Step 1.7.2.2

Cancel the common factor.

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

Step 1.7.2.3

Rewrite the expression.

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

Step 2

Simplify the denominator.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

One to any power is one.

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

Step 2.5

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

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

Step 2.6

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

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

Step 2.7

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

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

Step 2.8

Combine the numerators over the common denominator.

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

Step 2.9

Simplify the numerator.

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Step 2.9.1

Multiply $- 4$ by $4$ .

$\frac{\frac{3}{2}}{\frac{1 - 16}{4}}$

Step 2.9.2

Subtract $16$ from $1$ .

$\frac{\frac{3}{2}}{\frac{- 15}{4}}$

Step 2.10

Move the negative in front of the fraction.

$\frac{\frac{3}{2}}{- \frac{15}{4}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{3}{2} (- \frac{4}{15})$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Move the leading negative in $- \frac{4}{15}$ into the numerator.

$\frac{3}{2} \cdot \frac{- 4}{15}$

Step 4.2

Factor $3$ out of $15$ .

$\frac{3}{2} \cdot \frac{- 4}{3 (5)}$

Step 4.3

Cancel the common factor.

$\frac{3}{2} \cdot \frac{- 4}{3 \cdot 5}$

Step 4.4

Rewrite the expression.

$\frac{1}{2} \cdot \frac{- 4}{5}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $- 4$ .

$\frac{1}{2} \cdot \frac{2 (- 2)}{5}$

Step 5.2

Cancel the common factor.

$\frac{1}{2} \cdot \frac{2 \cdot - 2}{5}$

Step 5.3

Rewrite the expression.

$\frac{- 2}{5}$

Step 6

Move the negative in front of the fraction.

$- \frac{2}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{5}$

Decimal Form:

$- 0.4$