Solve -5/2+3/frac{5{2}-4}

$$\frac { - \frac { 5 } { 2 } + 3 } { \frac { 5 } { 2 } - 4 }$$

Evaluate

$$-\frac{1}{3}\approx -0.333333333$$

Solution Steps

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

$$\frac{-\frac{5}{2}+\frac{6}{2}}{\frac{5}{2}-4}$$

Since -\frac{5}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-5+6}{2}}{\frac{5}{2}-4}$$

Add -5 and 6 to get 1.

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

Convert 4 to fraction \frac{8}{2}.

$$\frac{\frac{1}{2}}{\frac{5}{2}-\frac{8}{2}}$$

Since \frac{5}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{2}}{\frac{5-8}{2}}$$

Subtract 8 from 5 to get -3.

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

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

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

Multiply \frac{1}{2} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-2\right)}{2\times 3}.

$$\frac{-2}{6}$$

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

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

Factor

$$-\frac{1}{3} = -0.3333333333333333$$