If both `a\ a n d\ b` are rational numbers, find the values of `a\ a n d\ b` in each of the following equalities: `(sqrt(2)+\ sqrt(3))/(3sqrt(2\ )-\ 2sqrt(3))=a-b\ sqrt(6)`

Explanation

Given that,LHS
=`(√2+√3)/(3√2-2√3)`
=`(√2+√3)/(3√2-2√3)'×(3√2+2√3)/(3√2+2√3)`
=`[(√2+√3)(3√2+2√3)]/[(3√2-2√3)(3√2+2√3)]`
=`[12+(2+3)√6]/6`
=`[12+5√6]/6`
=`[12/6]+[5√6]/6`
Now, in RHS=`a-b√6`
From LHS and RHS, we have:`2 + 3√6`
=`a−b√6` So,we get :`a`
=`12` and `b`=`-5/6`.