Question

x=root 3+root 2/root 3-root 2 and y=1 so x-y/x-3y=?​

Answer 1

Correct answer is $= \frac{( 4 + \sqrt{6})}{5}$

Explanation:

Given that, $y = 1$

$x = \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}$

On rationalizing the above equation,

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

$x = 5 + 2\sqrt{6}$

Now, $\frac{x - y}{x - 3y}$ $= \frac{ 5 + 2 \sqrt{6} - 1}{ 5 + 2\sqrt{6} - 3}$

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

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

$= \frac{(- 4 - \sqrt{6})}{- 5}$

Correct answer is $= \frac{( 4 + \sqrt{6})}{5}$.