7:50 am

The idea of simplification is that of forming a rational expression that combines all of the terms in the original expression.

There are a number of algebraic "facts" that I no longer remember. For example, I knew that there was an expression for a^3 - b^3, but I had forgotten exactly what it was. Now I know it.

This is relatively slow slogging at the moment, but I am confident that it will pay dividends later as I do need some practice with manipulating the relationships. There is a difference between simply understanding that a rational expression is simply a quotient involving two simpler expressions and being able to work with such expressions. I have the concept, but my technical skills are much weaker.

There are analogies with young children who are first learning basic arithmetic. But in this case the situation is often the reverse: they are able to say that 5 + 3 is 8, but they are not really aware of the idea of addition (or division).

Imagine having a 10 x 10 table of abstract symbols (e.g. Egyptian, or Mayan, hieroglyphics) and being told you had to memorize it! No wonder children have difficulty.

Rats! I keep forgetting to stamp my work with my red Japanese symbol and my green turtle icon.