Evaluate 1/2+8/(1/2-1)

$\frac{1}{2} + \frac{8}{\frac{1}{2} - 1}$

Simplify each term.

Simplify the denominator.

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2} + \frac{8}{\frac{1}{2} - 1 \cdot \frac{2}{2}}$

Combine $- 1$ and $\frac{2}{2}$ .

$\frac{1}{2} + \frac{8}{\frac{1}{2} + \frac{- 1 \cdot 2}{2}}$

Combine the numerators over the common denominator.

$\frac{1}{2} + \frac{8}{\frac{1 - 1 \cdot 2}{2}}$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$\frac{1}{2} + \frac{8}{\frac{1 - 2}{2}}$

Subtract $2$ from $1$ .

$\frac{1}{2} + \frac{8}{\frac{- 1}{2}}$

Move the negative in front of the fraction.

$\frac{1}{2} + \frac{8}{- \frac{1}{2}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} + 8 (- 1 \cdot 2)$

Multiply $- 1$ by $2$ .

$\frac{1}{2} + 8 \cdot - 2$

Multiply $8$ by $- 2$ .

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

To write $- 16$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2} - 16 \cdot \frac{2}{2}$

Combine $- 16$ and $\frac{2}{2}$ .

$\frac{1}{2} + \frac{- 16 \cdot 2}{2}$

Combine the numerators over the common denominator.

$\frac{1 - 16 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 16$ by $2$ .

$\frac{1 - 32}{2}$

Subtract $32$ from $1$ .

$\frac{- 31}{2}$

Move the negative in front of the fraction.

$- \frac{31}{2}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{31}{2}$

Decimal Form:

$- 15.5$

Mixed Number Form:

$- 15 \frac{1}{2}$