Solve 6.5/x/sqrt{3/2}

$$\frac{ \frac{ 6.5 }{ x } }{ \frac{ \sqrt{ 3 } }{ 2 } }$$

Evaluate

$$\frac{13\sqrt{3}}{3x}$$

Solution Steps

Divide \frac{6.5}{x} by \frac{\sqrt{3}}{2} by multiplying \frac{6.5}{x} by the reciprocal of \frac{\sqrt{3}}{2}.

$$\frac{6.5\times 2}{x\sqrt{3}}$$

Multiply 6.5 and 2 to get 13.

$$\frac{13}{x\sqrt{3}}$$

Rationalize the denominator of \frac{13}{x\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{13\sqrt{3}}{x\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{13\sqrt{3}}{x\times 3}$$

Differentiate w.r.t. x

$$-\frac{13\sqrt{3}}{3x^{2}}$$