## An Experiment with Wolfram|Alpha

I have been thinking about equal signs lately (The subject of a forthcoming blog entry) and decided to see what Wolfram|Alpha thought.  Here is my first try.

Wolfram|Alpha Equal Signs - No Instructions

If you give Wolfram|Alpha an equation like $\frac{x^2-4}{x-2}=x+2$ without instructions, it responds with the  statement “True”.  Essentially it tries to prove an identity and it makes a mistake.  The equation  is not defined for $x=2$.

If you give Wolfram|Alpha the instructions to show or prove the same equation, you get a similar result, still incorrect.

Wolfram|Alpha - Equal Signs - Show

Wolfram|Alpha Equal Signs - Prove

If you give Wolfram|Alpha instructions to solve the same equality.  You get the following.

Wolfram|Alpha Equal Signs - Solve

This is also incorrect.  Since the expression on the left is undefined for $x=2$, “all values of x” are not solutions.

These questions don’t  strike me as  too sophisticated  to ask Wolfram|Alpha.  That fact the expression $\frac{x^2-4}{x-2}$ is undefined at $x=2$ is fundamental to our discussions when we introduce function domains in college algebra and plays a large part in the discussion of limits in calculus.  I am disappointed.