Question

Prove This
1/ 2−√3 − 1/ √3−√2 + 1/ √2−1 = 3.​

Answer 1

Answer:

Step-by-step explanation:

question says

$\frac{1}{2-\sqrt{3} } - \frac{1}{\sqrt{3} - \sqrt{2} } + \frac{1}{\sqrt{2} - 1}$

we can rationalize each of the denominator as

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

which will give us

$\frac{2 + \sqrt{3} }{4-3} - \frac{\sqrt{3} + \sqrt{2} }{3-2} +\frac{\sqrt{2} + 1 }{2-1}$

$(2+\sqrt{3}) - (\sqrt{3}+\sqrt{2} ) +(\sqrt{2} +1)\\2+\sqrt{3}-\sqrt{3}-\sqrt{2}+\sqrt{2}+1\\2+1\\3$