Today's soundtrack is Proximity Seven: To the Ocean, the demo album of a rock band that I saw at a Battle of the Bands competition circa 2005.
This afternoon, I worked on the assignment portion of this lesson. I made it halfway through the assignment. While working, I figured out a couple of new things about equivalent rational expressions:
1) x+2 / x+1 can't be simplified to 2, but 2x / x can. The reason for this is that though we can multiply or subtract identical values from numerator and denominator to find equivalent values, we cannot add or subtract values.
2) The reason that we can multiply or divide both numerator and denominator by the "same non-zero factor" (Pearson's Pre-Calculus 11, p. 527) and get an equivalent form of a rational expression is that the values will scale relative to their initial values, so the ratio will remain intact.
That's all the time I have for today; next time, I'll try to finish up this assignment.