Question

Simplify by rationalizing the denominator :
​

Answer 1

Step-by-step explanation:

2√6-√5/3√5-2√6.

NOW,, RATIONALIZE THE FRACTION..

; (2√6-√5)(3√5+2√6)/(3√5)^2 - (2√6)^2.

; 6√30+24-15-2√30/(3√5)^2 - (2√6)^2.

; 4√30+9/45-24.

; 4√30+9/21.

HOPE IT WILL BE HELPFUL!!

Answer 2

$\huge\boxed{\underline{\bf { \red S \green O \pink L \blue U \orange T \purple I \red O \pink N \green{..}}}}$

$\longmapsto \sf \frac{2 \sqrt{6} - \sqrt{5} }{3 \sqrt{5} - 2 \sqrt{6}}$

$\longmapsto \sf\frac{2 \sqrt{6} - \sqrt{5} }{3 \sqrt{5} - 2 \sqrt{6}} \times \frac{3 \sqrt{5} + 2 \sqrt{6}}{3 \sqrt{5}+2 \sqrt{6}}$

$\longmapsto \sf\frac{6 \sqrt{30} + 4 \sqrt{36} - 3 \sqrt{25} - 2 \sqrt{30}}{ {(3 \sqrt{5}) }^{2} - {(2 \sqrt{6} )}^{2} }$

$\longmapsto \sf\frac{6 \sqrt{30} + 24- 15 - 2 \sqrt{30}}{ 45 - 24 }$

$\longmapsto \sf\frac{6 \sqrt{30} + 24- 15 - 2 \sqrt{30}}{21}$

$\longmapsto \sf\frac{6 \sqrt{30} +9 - 2 \sqrt{30}}{ 21 }$