Evaluate 1/(8+1/(12+1/15))

$\frac{1}{8 + \frac{1}{12 + \frac{1}{15}}}$

Simplify the denominator.

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To write $12$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{1}{8 + \frac{1}{12 \cdot \frac{15}{15} + \frac{1}{15}}}$

Combine $12$ and $\frac{15}{15}$ .

$\frac{1}{8 + \frac{1}{\frac{12 \cdot 15}{15} + \frac{1}{15}}}$

Combine the numerators over the common denominator.

$\frac{1}{8 + \frac{1}{\frac{12 \cdot 15 + 1}{15}}}$

Simplify the numerator.

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Multiply $12$ by $15$ .

$\frac{1}{8 + \frac{1}{\frac{180 + 1}{15}}}$

Add $180$ and $1$ .

$\frac{1}{8 + \frac{1}{\frac{181}{15}}}$

Simplify the denominator.

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Simplify each term.

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Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{8 + 1 (\frac{15}{181})}$

Multiply $\frac{15}{181}$ by $1$ .

$\frac{1}{8 + \frac{15}{181}}$

To write $8$ as a fraction with a common denominator, multiply by $\frac{181}{181}$ .

$\frac{1}{8 \cdot \frac{181}{181} + \frac{15}{181}}$

Combine $8$ and $\frac{181}{181}$ .

$\frac{1}{\frac{8 \cdot 181}{181} + \frac{15}{181}}$

Combine the numerators over the common denominator.

$\frac{1}{\frac{8 \cdot 181 + 15}{181}}$

Simplify the numerator.

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Multiply $8$ by $181$ .

$\frac{1}{\frac{1448 + 15}{181}}$

Add $1448$ and $15$ .

$\frac{1}{\frac{1463}{181}}$

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{181}{1463})$

Multiply $\frac{181}{1463}$ by $1$ .

$\frac{181}{1463}$

The result can be shown in multiple forms.

Exact Form:

$\frac{181}{1463}$

Decimal Form:

$0.12371838 \dots$

Evaluate 1/(8+1/(12+1/15))