Solve (72x^3 - 18x)/(12x^2 - 6x) = 0 for x.

So first you need to recognise that you are able to take 2x out of both the numerator and denominator of the fraction:(72x3 - 18x)/(12x2 - 6x) = 0 ---> (2x (36x² - 9))/ (2x (6x - 3)) = 0 , the 2x's cancel and we are left with (36x² - 9)/ (6x - 3)= 0 , from here it is necessary to identify that the numerator can be factorised by the difference of two squares: (6x - 3)(6x + 3)/ (6x - 3)= 0 , the (6x-3) brackets cancel and we are left with the simple equation, 6x+3 = 0, which is solved for x to be, x = -1/2.