Simply RREF means that you must find a way to transform the coefficients matrix into the identity matrix of the same order (if your system is of order 3x3, then you must end up with an 3x3 identity). There are cases in which you cannot fully transform the coefficients matrix into the identity matrix, but you can get close. Try reading something about elementary operations.

First of all, you must start with 1 in the first entry ( ). But why? Because you want to cancel the numbers below the first entry, that is, turn all the other numbers of the same column into zeros (and having 1 in the first entry makes it more simple to do).

In your case, you can either divide the first line by 2 or you can exchange the third line with the first.

Suppose that you exchange lines for preventing the division. Now you have

1 3/2 9/2 :5

0 1 3 :5

2 1 3 :0

As you want all zeros, you must eliminate the first entry in the third line. You multiply the first line by 2 and subtract it with the third line (but you mantain the first line). So:

1 3/2 9/2 :5

0 1 3 :5

0 -2 -6 :-10

Now you have to make zeros appear in the second column, but leaving 1 in the second entry of the second row , and then the same thing with the third column (leaving . Can you do this by yourself now?