Evaluate (3(-1/2)^2)/((-1/2)^2-4)

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

Simplify the numerator.

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

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

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

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

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

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

One to any power is one.

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

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

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

Combine exponents.

Multiply $3$ by $1$ .

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

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

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

Simplify the denominator.

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

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

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

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

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

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

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

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

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

One to any power is one.

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 4$ by $4$ .

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

Subtract $16$ from $1$ .

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

Move the negative in front of the fraction.

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

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor of $3$ .

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

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

Factor $3$ out of $15$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

$\frac{1}{4} \cdot \frac{4 (- 1)}{5}$

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 1}{5}$

Move the negative in front of the fraction.

$- \frac{1}{5}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{5}$

Decimal Form:

$- 0.2$

Evaluate (3(-1/2)^2)/((-1/2)^2-4)

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