Solve -1/2-sqrt{3}

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

Evaluate

$$-\sqrt{3}-2\approx -3.732050808$$

Solution Steps

Rationalize the denominator of \frac{1}{2-\sqrt{3}} by multiplying numerator and denominator by 2+\sqrt{3}.

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

Consider \left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Square 2. Square \sqrt{3}.

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

Subtract 3 from 4 to get 1.

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

Anything divided by one gives itself.

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

To find the opposite of 2+\sqrt{3}, find the opposite of each term.

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