Solve 1/2-1/frac{3{2}+1}div3/2-1/frac{1{2}+1}

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

Evaluate

$$-\frac{3}{5}=-0.6$$

Solution Steps

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

$$\frac{\left(\frac{1}{2}-1\right)\left(\frac{1}{2}+1\right)}{\left(\frac{3}{2}+1\right)\left(\frac{3}{2}-1\right)}$$

Extract the negative sign in \frac{1}{2}-1.

$$\frac{-\left(\frac{3}{2}-1\right)\left(\frac{1}{2}+1\right)}{\left(\frac{3}{2}-1\right)\left(1+\frac{3}{2}\right)}$$

Cancel out \frac{3}{2}-1 in both numerator and denominator.

$$\frac{-\left(\frac{1}{2}+1\right)}{1+\frac{3}{2}}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{-\left(\frac{1}{2}+\frac{2}{2}\right)}{1+\frac{3}{2}}$$

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

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

Add 1 and 2 to get 3.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

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

Add 2 and 3 to get 5.

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

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

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

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

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

Cancel out 2 in both numerator and denominator.

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

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

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

Factor

$$-\frac{3}{5} = -0.6$$