How can you test the equivalance of two expressions?

Answer 1

You can check for a few numbers, to see whether they give you the same result. This quick check can save you lots of work in the following step, in the case of complicated expressions: if, when replacing by some number, the two expressions are NOT equal, then of course they are not equivalent.However, the variables can usually have infinitely many values (Boolean algebra is an exception), in which case the only way to prove that two expressions are equivalent - meaning, equal for ALL values of the variable or variables - is to try to do some equivalence transformation to one expression, to convert it to the other expression.

Answer 2

Further to the answer given by Hilmarz, if E1 and E2 are the two expressions then two equivalence transformations that you may wish to try are

• E1 - E2 = 0
• E1/E2 = 1

In some situations one will be simpler than the other. There are other tests.