Question

simplify 2√3-1 by (√3-1)and then express it with

rational denominator​

Answer 1

Answer:

$\dfrac{ \ \sqrt{3} - 6}{6}$

Step-by-step explanation:

Given:

$\dfrac{2 \sqrt{3} - 1}{ {( \sqrt{3} - 1) }^{2} - 4}$

To do:

Simplify and Express the given with a rational

denominator.

Solution:

$\frac{2 \sqrt{3} - 1}{ {( \sqrt{3} - 1) }^{2} - 4} \\ \\ = \frac{2 \sqrt{3} - 1}{ { (\sqrt{3} )}^{2} + 2 .\sqrt{3} .1 + {1}^{2} - 4 } \\ \\ = \frac{2 \sqrt{3} - 1 }{3 + 1 - 2 \sqrt{3} - 4} \\ \\ = \frac{2 \sqrt{3} - 1}{4 - 4 - 2 \sqrt{3} } \\ \\ = \frac{(2 \sqrt{3} - 1) \sqrt{3} }{ - 2 \sqrt{3} \times \sqrt{3} } \\ \\ = \frac{2 .3 - \sqrt{3} }{ - 2.3} \\ \\ = \frac{6 - \sqrt{3} }{ - 6} \\ \\ = \frac{ \sqrt{3} - 6 }{6}$