Question

simplify
root 13 -root 11 /root 13 +root 11 + root 13 +root 11/root 13 -root 11

Answer 1

Hi

(√13-√11)/(√13+√11)+(√13+√11)/(√13-√11)

= [(√13-√11)²+(√13+√11)²]/[(√13+√11)(√13-√11)]

= { 2[ (√13)²+(√11)²]}/[ (√13 )² - ( √11 )² ]

= [ 2( 13 + 11 ) ] / ( 13 - 11 )

= [ 2 × 24 ]/ 2

= 24

I hope this helps you.

: )

Answer 2

Answer:

24

Step-by-step explanation:

Given expression is,

$\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}+\sqrt{11}} + \frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}}$

$=\frac{(\sqrt{13}-\sqrt{11})^2+(\sqrt{13}+\sqrt{11})^2 }{(\sqrt{13})^2-(\sqrt{11})^2}$

$=\frac{13+11-2\sqrt{143}+13+11+2\sqrt{143} }{13-11}$

( Since, (a±b)² = a² ±2ab + b² )

$=\frac{48 }{2}$

$=24$