1/(√7-1)-1/(√7-3)=a+b√c
[√7-3-(√7-1)]/(10-4√7)=a+b√c
(1-3)/(10-4√7)=a+b√c
-2/2(5-2√7)=a+b√c
-1/(5-2√7)=a+b√c
-(5+2√7)/(25-28)=a+b√c
-(5+2√7)/-3=a+b√c
5/3+2/3√7=a+b√c
a=5/3 b=⅔ c=√7/3
Is this correct
very good until your last step
5/3+2/3√7=a+b√c
a=5/3 b=⅔ c=7