Question

Simplify the expression. itle="\frac{6}{1+\sqrt{3} }" alt="\frac{6}{1+\sqrt{3} }" align="absmiddle" class="latex-formula">

Answer 1

Answer:

Step-by-step explanation:

Rationalize the denominator by multiplying both denominator & numerator by the conjugate of the denominator.

Conjugate of the denominator  1 + √3 is 1 - √3

$\frac{6}{1+\sqrt{3}}=\frac{6(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\=\frac{6(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\=\frac{6(1-\sqrt{3})}{1^{2}-(\sqrt{3})^{2}}\\\\=\frac{6(1-\sqrt{3})}{1-3}\\\\=\frac{6(1-\sqrt{3})}{-2}\\\\=(-3)(1-\sqrt{3})\\\\=-3+3\sqrt{3}$