Solve 1/frac{frac{1{2}+3}{1/2-6}}

$$\frac{ 1 }{ \frac{ \frac{ 1 }{ 2 } +3 }{ \frac{ 1 }{ 2 } -6 } }$$

Evaluate

$$-\frac{11}{7}\approx -1.571428571$$

Solution Steps

Divide 1 by \frac{\frac{1}{2}+3}{\frac{1}{2}-6} by multiplying 1 by the reciprocal of \frac{\frac{1}{2}+3}{\frac{1}{2}-6}.

$$\frac{\frac{1}{2}-6}{\frac{1}{2}+3}$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{\frac{1}{2}-\frac{12}{2}}{\frac{1}{2}+3}$$

Since \frac{1}{2} and \frac{12}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-12}{2}}{\frac{1}{2}+3}$$

Subtract 12 from 1 to get -11.

$$\frac{-\frac{11}{2}}{\frac{1}{2}+3}$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{-\frac{11}{2}}{\frac{1}{2}+\frac{6}{2}}$$

Since \frac{1}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{11}{2}}{\frac{1+6}{2}}$$

Add 1 and 6 to get 7.

$$\frac{-\frac{11}{2}}{\frac{7}{2}}$$

Divide -\frac{11}{2} by \frac{7}{2} by multiplying -\frac{11}{2} by the reciprocal of \frac{7}{2}.

$$-\frac{11}{2}\times \frac{2}{7}$$

Multiply -\frac{11}{2} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-11\times 2}{2\times 7}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-11}{7}$$

Fraction \frac{-11}{7} can be rewritten as -\frac{11}{7} by extracting the negative sign.

$$-\frac{11}{7}$$

Factor

$$-\frac{11}{7} = -1\frac{4}{7} = -1.5714285714285714$$