Question

What is the standard form of (1+2sgrt-3)/(1+sgrt-3)?

Answer 1

Answer:

$\large \boxed{\sf \ \ \dfrac{5-\sqrt{3}}{2} \ \ }$

Step-by-step explanation:

Hello,

$\dfrac{1+2\sqrt{3}}{1+\sqrt{3}}=\dfrac{(1+2\sqrt{3})(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\ \text{... to eliminate the root in the denominator ...} \\\\=\dfrac{1-\sqrt{3}+2\sqrt{3}-2*3}{(1-3)}\\\\=-\dfrac{1+\sqrt{3}-6}{2}\\\\=-\dfrac{\sqrt{3}-5}{2}\\\\=\dfrac{5-\sqrt{3}}{2}$

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