Rational Equation Problem

a/(2a-6) - 3/(a^2-6a+9) = (a-2)/(3a-9)

a/(2(a-3)) -3/((a-3)(a-3)) = (a-2)/(3(a-3))

multiply all terms by (a-3)

a/2 - 3/(a-3) = (a-2)/3

multiply by 6(a-3)

3a(a-3) -3*6=2(a-2)(a-3)

3a^2-9a-18=2a^2-10a+12

a^2+a-30=0

(a+6)(a-5)=0

a+6=0 or a-5=0

Answer: a=-6 or a=5

You can check these answers using @ :

a/(2a-6) - 3/(a^2-6a+9) = (a-2)/(3a-9) @ -6