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

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

Evaluate

$$-\frac{5}{3}\approx -1.666666667$$

Solution Steps

Convert 2 to fraction \frac{4}{2}.

$$\frac{\frac{1}{2}+\frac{4}{2}}{\frac{1}{2}-2}$$

Since \frac{1}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+4}{2}}{\frac{1}{2}-2}$$

Add 1 and 4 to get 5.

$$\frac{\frac{5}{2}}{\frac{1}{2}-2}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{\frac{5}{2}}{\frac{1}{2}-\frac{4}{2}}$$

Since \frac{1}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{2}}{\frac{1-4}{2}}$$

Subtract 4 from 1 to get -3.

$$\frac{\frac{5}{2}}{-\frac{3}{2}}$$

Divide \frac{5}{2} by -\frac{3}{2} by multiplying \frac{5}{2} by the reciprocal of -\frac{3}{2}.

$$\frac{5}{2}\left(-\frac{2}{3}\right)$$

Multiply \frac{5}{2} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-2\right)}{2\times 3}$$

Do the multiplications in the fraction \frac{5\left(-2\right)}{2\times 3}.

$$\frac{-10}{6}$$

Reduce the fraction \frac{-10}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{3}$$

Factor

$$-\frac{5}{3} = -1\frac{2}{3} = -1.6666666666666667$$