Solve 12/99+frac{1/frac{12{12}}-1}{{left(12/99right)}^2+1/frac{12{99}}}

$$\frac{ \frac{ 12 }{ 99 } + \frac{ 1 }{ \frac{ 12 }{ 12 } } -1 }{ { \left( \frac{ 12 }{ 99 } \right) }^{ 2 } + \frac{ 1 }{ \frac{ 12 }{ 99 } } }$$

Evaluate

$$\frac{528}{36001}\approx 0.014666259$$

Solution Steps

Divide 12 by 12 to get 1.

$$\frac{\frac{12}{99}+\frac{1}{1}-1}{\left(\frac{12}{99}\right)^{2}+\frac{1}{\frac{12}{99}}}$$

Divide 1 by 1 to get 1.

$$\frac{\frac{12}{99}+1-1}{\left(\frac{12}{99}\right)^{2}+\frac{1}{\frac{12}{99}}}$$

Reduce the fraction \frac{12}{99} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{4}{33}+1-1}{\left(\frac{12}{99}\right)^{2}+\frac{1}{\frac{12}{99}}}$$

Add \frac{4}{33} and 1 to get \frac{37}{33}.

$$\frac{\frac{37}{33}-1}{\left(\frac{12}{99}\right)^{2}+\frac{1}{\frac{12}{99}}}$$

Subtract 1 from \frac{37}{33} to get \frac{4}{33}.

$$\frac{\frac{4}{33}}{\left(\frac{12}{99}\right)^{2}+\frac{1}{\frac{12}{99}}}$$

Reduce the fraction \frac{12}{99} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{4}{33}}{\left(\frac{4}{33}\right)^{2}+\frac{1}{\frac{12}{99}}}$$

Calculate \frac{4}{33} to the power of 2 and get \frac{16}{1089}.

$$\frac{\frac{4}{33}}{\frac{16}{1089}+\frac{1}{\frac{12}{99}}}$$

Divide 1 by \frac{12}{99} by multiplying 1 by the reciprocal of \frac{12}{99}.

$$\frac{\frac{4}{33}}{\frac{16}{1089}+\frac{99}{12}}$$

Reduce the fraction \frac{99}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{4}{33}}{\frac{16}{1089}+\frac{33}{4}}$$

Add \frac{16}{1089} and \frac{33}{4} to get \frac{36001}{4356}.

$$\frac{\frac{4}{33}}{\frac{36001}{4356}}$$

Divide \frac{4}{33} by \frac{36001}{4356} by multiplying \frac{4}{33} by the reciprocal of \frac{36001}{4356}.

$$\frac{4}{33}\times \frac{4356}{36001}$$

Multiply \frac{4}{33} and \frac{4356}{36001} to get \frac{528}{36001}.

$$\frac{528}{36001}$$

Factor

$$\frac{2 ^ {4} \cdot 3 \cdot 11}{7 \cdot 37 \cdot 139} = 0.014666259270575818$$