Factor each denominator.

2x – 6 = 2(x-3)

x^2 -6x +9 = (x-3)(x-3) = (x-3)^2

3x-9 = 3(x-3)

Multiply everything by 6(x-3)^2

3x(x-3) – 3(6) = (x-2)(2)(x-3)

Simplify

3x^2 – 9x – 18 = 2(x^2 -5x +6)

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

Move everything to one side

x^2 + x – 30 = 0

Factor

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

x = -6 or x = 5

Follow the above steps for the second one.

Then group the like terms and simplify them; if there are two or more terms that are the same power of x and have the same denominator

Then find common denominators for the fractions and combine.

Then see if you can find a way to factor any part of the equation. If you have a quadratic equation somewhere that can be factored, do it after isolating it on one side of the equation.

This kind of problem has to be chipped away at, little by little.