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find the value of a and b if

5+root6 divided by 5-root 6=a+b root6

please explain me .

$\frac{5 + \sqrt{6}}{5 - \sqrt{6}} = a + b \sqrt{6} O n r a t i o n a l i z in g t h e L H S, w e g e t, \Rightarrow \frac{5 + \sqrt{6}}{5 - \sqrt{6}} \times \frac{5 + \sqrt{6}}{5 + \sqrt{6}} = a + b \sqrt{6} \Rightarrow \frac{(5 + \sqrt{6}) (5 + \sqrt{6})}{(5 - \sqrt{6}) (5 + \sqrt{6})} = a + b \sqrt{6} \Rightarrow \frac{(5 + \sqrt{6}) (5 + \sqrt{6})}{{(5)}^{2} - {(\sqrt{6})}^{2}} = a + b \sqrt{6} \Rightarrow \frac{25 + 10 \sqrt{6} + 6}{25 - 6} = a + b \sqrt{6} \Rightarrow \frac{31 + 10 \sqrt{6}}{19} = a + b \sqrt{6} i t c a n a l s o b e w r i t t e n a s, \Rightarrow \frac{31}{19} + \frac{10}{19} \sqrt{6} = a + b \sqrt{6} N o w, o n c o m p a r i n g b o t h s i d e s, w e g e t, \frac{31}{19} = a a n d \frac{10}{19} \sqrt{6} = b \sqrt{6} \Rightarrow a = \frac{31}{19} & b = \frac{10}{19}$

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