Question

how would you check that 1/3x is the quotient of (6x^2/24x)/(4x^3/12x)?

Answer 1

To do a quick check, you can graph each expression separately. If the two graphs line up perfectly, then the two are identical (and therefore the same).

Answer 2

what about a way through equation?

Answer 3

Well you can try this


You basically want the two expressions. So you want to show that


(6x^2/24x)/(4x^3/12x) = 1/3x


is true for all allowed values of x


So if you solve that equation, you should get something like 0 = 0, which would imply that there are an infinite number of solutions (which would mean that the two sides are the same)