Solve frac{sqrt{3}}{(2+sqrt{3})(2-sqrt{3})}

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

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

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}.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{\sqrt{3}}{4-\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

Subtract 3 from 4 to get 1.

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

Anything divided by one gives itself.

$$\sqrt{3}$$