Today's soundtrack is Plankeye: Strange Exchange, an album that I bought in the early 2ks after hearing their single "The Meaning of it All" on a compilation CD, Tooth and Nail Records' "Cheapskates Vol. 2."
This morning, I'm continuing to work on the assignment portion of the Multiplying and Dividing Rational Expressions lesson. Links to previous sessions:
So, yesterday's session was a massive grind that left me exhausted and discouraged. Like I mentioned last night, I was getting frustrated because it felt like the goalpost kept changing. How far did they want me to factor this time? Which common factors was I supposed to pick?
Something had to give. I could tell that something was missing in my foundational understandings of the concepts I was trying to work on, but I didn't know where the gap was. I decided to sign up for Wolfram|Alpha pro this morning so that I could use their "step-by-step" hint system and figure out what I was doing wrong. I'm pretty sure this is some of the best money I've spent on anything, because their method of showing alternate "hint/shown, hint/shown" in the step-by-step section is brilliant and exactly what I needed.
There were two major problems I was able to identify. First, I needed to rearrange the terms so that the highest-powered terms preceded the other terms. Next, I needed to be able to recognize that (x² + 1) is a difference of squares expression that should be factored as (x+1)(x-1). Also, I realized that I'd missed some steps in decomposition of factors when factoring trinomials!
After a bit of practice with their examples, I was able to do this one totally solo:
Thank you, Wolfram|Alpha!
*Edit: I'm finally done this chapter. Thank goodness. Next time, I'll be working on adding and subtracting rational expressions!
Disclaimer: I am not endorsed by or affiliated with Wolfram|Alpha. I am just really impressed with the product that they offer.