#1**+2 **

We can immediately see by inspection that when 2x - 3 = 0, both sides of the equation are zero.

This gives us our first soution: 2x - 3 =0 so x = 3/2

Now divide through by 2x - 3 (which we can do for the other solutions where 2x - 3 is not zero).

We are left with (2x - 3)^{2} = 4(2x - 3) - 3

Let u = 2x - 3, substitute in to the above and rearrange to get: u^{2} - 4u + 3 = 0

This quadratic factorises as (u - 1)(u - 3) = 0, giving u = 1 and u = 3

These, in turn, give: 2x - 3 = 1 means x = 2, and 2x - 3 = 3 means x = 3.

Alan Aug 31, 2020