Question

if [3/root 3 + 1]+[5/root 3 - 1] = a+b root 3

Answer 1

[3/√3+1]+[5/√3-1]=8/√3
multiply and divide by root3
=8√3/3
=5√3+3√3/3
=5/√3+√3
a=5/√3,b=1

Answer 2

$=\frac{3}{ \sqrt{3}+1 } + \frac{5}{ \sqrt{3}-1 }$

$=\frac{3( \sqrt{3} -1)+5( \sqrt{3}+1 )}{ (\sqrt{3}+1)( \sqrt{3}-1 ) }$

$=\frac{ 8 \sqrt{3} )}{ 2 }$

$=4 \sqrt{3}$

So, 
a=0 and b=4 by comparing


[3/√3+1]+[5/√3-1]=8/√3
multiply and divide by root3
=8√3/3
=5√3+3√3/3
=5/√3+√3
a=5/√3,b=1