Solve 3/4+1/6/1-(frac{3{4})(1/6)}-frac{frac{3}{4}(frac{1}{6})^2}{1-(frac{3}{4})(frac{1}{6})}

$$\frac { \frac { 3 } { 4 } + \frac { 1 } { 6 } } { 1 - ( \frac { 3 } { 4 } ) ( \frac { 1 } { 6 } ) } - \frac { \frac { 3 } { 4 } ( \frac { 1 } { 6 } ) ^ { 2 } } { 1 - ( \frac { 3 } { 4 } ) ( \frac { 1 } { 6 } ) }$$

Evaluate

$$\frac{43}{42}\approx 1.023809524$$

Solution Steps

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{\frac{9}{12}+\frac{2}{12}}{1-\frac{3}{4}\times \frac{1}{6}}-\frac{\frac{3}{4}\times \left(\frac{1}{6}\right)^{2}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+2}{12}}{1-\frac{3}{4}\times \frac{1}{6}}-\frac{\frac{3}{4}\times \left(\frac{1}{6}\right)^{2}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Add 9 and 2 to get 11.

$$\frac{\frac{11}{12}}{1-\frac{3}{4}\times \frac{1}{6}}-\frac{\frac{3}{4}\times \left(\frac{1}{6}\right)^{2}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Multiply \frac{3}{4} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{11}{12}}{1-\frac{3\times 1}{4\times 6}}-\frac{\frac{3}{4}\times \left(\frac{1}{6}\right)^{2}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 6}.

$$\frac{\frac{11}{12}}{1-\frac{3}{24}}-\frac{\frac{3}{4}\times \left(\frac{1}{6}\right)^{2}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{11}{12}}{1-\frac{1}{8}}-\frac{\frac{3}{4}\times \left(\frac{1}{6}\right)^{2}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{\frac{11}{12}}{\frac{8}{8}-\frac{1}{8}}-\frac{\frac{3}{4}\times \left(\frac{1}{6}\right)^{2}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Since \frac{8}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11}{12}}{\frac{8-1}{8}}-\frac{\frac{3}{4}\times \left(\frac{1}{6}\right)^{2}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Subtract 1 from 8 to get 7.

$$\frac{\frac{11}{12}}{\frac{7}{8}}-\frac{\frac{3}{4}\times \left(\frac{1}{6}\right)^{2}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Divide \frac{11}{12} by \frac{7}{8} by multiplying \frac{11}{12} by the reciprocal of \frac{7}{8}.

$$\frac{11}{12}\times \frac{8}{7}-\frac{\frac{3}{4}\times \left(\frac{1}{6}\right)^{2}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Multiply \frac{11}{12} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 8}{12\times 7}-\frac{\frac{3}{4}\times \left(\frac{1}{6}\right)^{2}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Do the multiplications in the fraction \frac{11\times 8}{12\times 7}.

$$\frac{88}{84}-\frac{\frac{3}{4}\times \left(\frac{1}{6}\right)^{2}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Reduce the fraction \frac{88}{84} to lowest terms by extracting and canceling out 4.

$$\frac{22}{21}-\frac{\frac{3}{4}\times \left(\frac{1}{6}\right)^{2}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$\frac{22}{21}-\frac{\frac{3}{4}\times \frac{1}{36}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Multiply \frac{3}{4} times \frac{1}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22}{21}-\frac{\frac{3\times 1}{4\times 36}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 36}.

$$\frac{22}{21}-\frac{\frac{3}{144}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Reduce the fraction \frac{3}{144} to lowest terms by extracting and canceling out 3.

$$\frac{22}{21}-\frac{\frac{1}{48}}{1-\frac{3}{4}\times \frac{1}{6}}$$

Multiply \frac{3}{4} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22}{21}-\frac{\frac{1}{48}}{1-\frac{3\times 1}{4\times 6}}$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 6}.

$$\frac{22}{21}-\frac{\frac{1}{48}}{1-\frac{3}{24}}$$

Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.

$$\frac{22}{21}-\frac{\frac{1}{48}}{1-\frac{1}{8}}$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{22}{21}-\frac{\frac{1}{48}}{\frac{8}{8}-\frac{1}{8}}$$

Since \frac{8}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22}{21}-\frac{\frac{1}{48}}{\frac{8-1}{8}}$$

Subtract 1 from 8 to get 7.

$$\frac{22}{21}-\frac{\frac{1}{48}}{\frac{7}{8}}$$

Divide \frac{1}{48} by \frac{7}{8} by multiplying \frac{1}{48} by the reciprocal of \frac{7}{8}.

$$\frac{22}{21}-\frac{1}{48}\times \frac{8}{7}$$

Multiply \frac{1}{48} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22}{21}-\frac{1\times 8}{48\times 7}$$

Do the multiplications in the fraction \frac{1\times 8}{48\times 7}.

$$\frac{22}{21}-\frac{8}{336}$$

Reduce the fraction \frac{8}{336} to lowest terms by extracting and canceling out 8.

$$\frac{22}{21}-\frac{1}{42}$$

Least common multiple of 21 and 42 is 42. Convert \frac{22}{21} and \frac{1}{42} to fractions with denominator 42.

$$\frac{44}{42}-\frac{1}{42}$$

Since \frac{44}{42} and \frac{1}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{44-1}{42}$$

Subtract 1 from 44 to get 43.

$$\frac{43}{42}$$

Factor

$$\frac{43}{2 \cdot 3 \cdot 7} = 1\frac{1}{42} = 1.0238095238095237$$