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.

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About jrh794

I am a sixty-five year old math instructor at Southern Oregon University. I taught at the College of the Siskiyous in Weed California for twenty-six years. Prior to that I worked as a computer programmer, carpenter and in various other jobs. I graduated from Rice University in 1967 and have a MS in Operations Research from Stanford. In the past I have hand-built a stone house and taken long solo bicycle tours. Now I ride my mountain bike and play golf for recreation.
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