What, exactly, do you mean by "prove an equation"? What do you mean by "it is not true"? Equations are typically true for some values of the variables and false for other. Often one either solves an equation (determines values of the unknowns so that the equation is true) or proves it is an identity (true for all possible values of the unknown). But then what are the "unknowns" and what are the constants?
If you are trying to solve the equation for x, that's easy. From ax+ b+ c= kbcx, subtract ax from both sides: kbcx- ax= (kbc- a)x= b+ c. Now, if kbc- a is not 0, that is if , . If kbc= a, there is no such x.
Or are you trying to prove that there exist numbers a and k so that this is true, no matter what x, b, and c? One thing you could do certainly is solve for a: . As long as x is not 0, given any values for b, c, x, and k, that gives a value of a that makes the equation true.
If you are trying to prove that is an "identity", true for all values of x, a, b, c, and k, that is obviously not true.