Evaluate -1/(8-1/8)

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

Simplify the denominator.

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To write $8$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

Combine $8$ and $\frac{8}{8}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Multiply $8$ by $8$ .

$- \frac{1}{\frac{64 - 1}{8}}$

Subtract $1$ from $64$ .

$- \frac{1}{\frac{63}{8}}$

Multiply the numerator by the reciprocal of the denominator.

$- (1 (\frac{8}{63}))$

Multiply $\frac{8}{63}$ by $1$ .

$- \frac{8}{63}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{8}{63}$

Decimal Form:

$- 0.\overline{126984}$

Evaluate -1/(8-1/8)