Alg2.1.19

Find the value of $\frac{1}{2+\sqrt{3}}+\frac{1}{2-\sqrt{3}}\,$

Rationalising the two fractions

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

Simplifying applying formulas

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

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

After simplifying the value of the given problem is

$4\,$