Evaluate (5(-1/2)^2)/((-1/2)^2-1)

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

Simplify the numerator.

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

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

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

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

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

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

One to any power is one.

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

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

$\frac{5 \cdot 1 \frac{1}{4}}{{(- \frac{1}{2})}^{2} - 1}$

Combine exponents.

Multiply $5$ by $1$ .

$\frac{5 (\frac{1}{4})}{{(- \frac{1}{2})}^{2} - 1}$

Combine $5$ and $\frac{1}{4}$ .

$\frac{\frac{5}{4}}{{(- \frac{1}{2})}^{2} - 1}$

Simplify the denominator.

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

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

$\frac{\frac{5}{4}}{{(- 1)}^{2} {(\frac{1}{2})}^{2} - 1}$

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

$\frac{\frac{5}{4}}{{(- 1)}^{2} \frac{1^{2}}{2^{2}} - 1}$

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

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

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

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

One to any power is one.

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 1$ by $4$ .

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

Subtract $4$ from $1$ .

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

Move the negative in front of the fraction.

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

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor of $4$ .

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

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

Factor $4$ out of $- 4$ .

$\frac{5}{4} \cdot \frac{4 (- 1)}{3}$

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 \cdot - 1}{3}$

Rewrite the expression.

$5 (\frac{- 1}{3})$

Combine $5$ and $\frac{- 1}{3}$ .

$\frac{5 \cdot - 1}{3}$

Simplify the expression.

Multiply $5$ by $- 1$ .

$\frac{- 5}{3}$

Move the negative in front of the fraction.

$- \frac{5}{3}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{3}$

Decimal Form:

$- 1.\overline{6}$

Mixed Number Form:

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

Evaluate (5(-1/2)^2)/((-1/2)^2-1)

Related Questions

Support LCMGCF.com by disabling your adblocker.