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

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

Evaluate

$$-\frac{6}{7}\approx -0.857142857$$

Solution Steps

Convert 5 to fraction \frac{10}{2}.

$$\frac{3}{\frac{3}{2}-\frac{10}{2}}$$

Since \frac{3}{2} and \frac{10}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{\frac{3-10}{2}}$$

Subtract 10 from 3 to get -7.

$$\frac{3}{-\frac{7}{2}}$$

Divide 3 by -\frac{7}{2} by multiplying 3 by the reciprocal of -\frac{7}{2}.

$$3\left(-\frac{2}{7}\right)$$

Express 3\left(-\frac{2}{7}\right) as a single fraction.

$$\frac{3\left(-2\right)}{7}$$

Multiply 3 and -2 to get -6.

$$\frac{-6}{7}$$

Fraction \frac{-6}{7} can be rewritten as -\frac{6}{7} by extracting the negative sign.

$$-\frac{6}{7}$$

Factor

$$-\frac{6}{7} = -0.8571428571428571$$