Solve 3/4sqrt{5}div-7/2sqrt{3}

$$\frac { 3 } { 4 } \sqrt { 5 } \div - \frac { 7 } { 2 } \sqrt { 3 }$$

Evaluate

$$-\frac{3\sqrt{15}}{14}\approx -0.829925003$$

Solution Steps

Divide \frac{3}{4}\sqrt{5} by -\frac{7}{2} by multiplying \frac{3}{4}\sqrt{5} by the reciprocal of -\frac{7}{2}.

$$\frac{\frac{3}{4}\sqrt{5}\times 2}{-7}\sqrt{3}$$

Express \frac{3}{4}\times 2 as a single fraction.

$$\frac{\frac{3\times 2}{4}\sqrt{5}}{-7}\sqrt{3}$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{6}{4}\sqrt{5}}{-7}\sqrt{3}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{2}\sqrt{5}}{-7}\sqrt{3}$$

Divide \frac{3}{2}\sqrt{5} by -7 to get -\frac{3}{14}\sqrt{5}.

$$-\frac{3}{14}\sqrt{5}\sqrt{3}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$-\frac{3}{14}\sqrt{15}$$