Question

Find a,b if 3+√7÷3-√7=a+b √7

Answer 1

3+√7 / 3-√7
multiply 3+√7 on both numerator and denomerator
(3+√7)² / (3-√7)(3+√7) = a+b√7
⇒9 + 7 + 6√7 / 3² -√7² = a+b√7
⇒16+ 6√7 / 9-7 =a+b√7
⇒16+ 6√7 / 2 =a+b√7
⇒2(8+3√7)/2 =a+b√7
⇒8 +3√7 =a+b√7

on compairing both sides
a=8
b=3