f(x) > g(x)

f(x) = x^2 -3x

g(x) = x-3

f(x) > g(x)

So we have that    f(x) > g(x)    means that

x^2 - 3x  >  x - 3       subtract x from both sides.....add 3 to both sides

x^2 - 3x - x + 3 >  0       factor

x (x -3)  - 1(x - 3) > 0   .......  (x - 3)  is the common factor

(x -1) (x -3) > 0    .......Set to 0

(x -1) ( x - 3)  = 0  

Setting each factor to 0  gives us the solutions of  x  = 1  and  x = 3

This tells us that the solutions will come from these possible intervals :

(-inf, 1) , (1, 3)   or (3, inf)   ........   test a point in the inequality (x -1) (x -3) > 0 in each interval

If x = 2, the inequality will be untrue

If x = 4 it will be true    and it will be true if x = 0

So.....the correct solutions are  :  (-inf, 1) U (3, inf)    or    x < 1  U   x > 3