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

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

Evaluate

$$-\frac{5\sqrt{3}}{3}+2\approx -0.886751346$$

Solution Steps

Rationalize the denominator of \frac{2\sqrt{3}-5}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(2\sqrt{3}-5\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(2\sqrt{3}-5\right)\sqrt{3}}{3}$$

Use the distributive property to multiply 2\sqrt{3}-5 by \sqrt{3}.

$$\frac{2\left(\sqrt{3}\right)^{2}-5\sqrt{3}}{3}$$

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

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