a/2+3/(a-3)=a/(a-3)
You want to make the common denominator (2a-6) which is 2(a-3) then you will have:
(a/2)((a-3)/(a-3))+(3*2)/(2(a-3))=2a/(2(a-3))
(a^2-3a)/(2a-6)+6/(2a-6)=2a/(2a-6) multiplying the equation by (2a-6) leaves
a^2-3a+6=2a
a^2-5a+6=0 now factor...
a^2-2a-3a+6=0
a(a-2)-3(a-2)=0
(a-3)(a-2)=0
So there are two solutions for the value of a:
a=2 and 3
