I received an SOS from my younger sister, who was stumped on an algebra problem. It’s actually not her homework — it’s her husband’s, who’s back in school (community college) to get his degree in order to be a building inspector.
But first, the algebra homework. He was stumped, she was stumped, and she called me for help, as I was driving home from work. She emailed me the problem, which I saw after dinner and a “Tadpole wants me to sleep” afternoon nap.
It really wasn’t hard. But *dang* if my “I’m an English professor now” forebrain get getting stumped because it’s been over ten years since I did math problems higher than high speed arithmetic (figuring out grades, paying bills, that sort of thing).
Thank God the Hubby had an Intermediate College Algebra textbook in the house so I could refresh my algebra memory. My lizard brain kept squealing, “You know this! You aced Calculus II for Godsakes!” while my forebrain replied, “Shut up you, and help me look up stuff in this book!”
After doing a couple of practice problems, it came back to place.
So here’s what I emailed back to my kid sister:
It’s been REALLY long since I’ve done College Algebra, but here’s what I got:
1/a + 1/b
1/a^2 – 1/b^2
= a^2*b^2 (1/a +1/b)
a^2*b^2 (1/a^2 – 1/b^2)
= ab^2 + a^2b
b^2 – a^2
= (b+a) ab
Feel free to check my work, but I think this is about as simplified as this solution gets. I multiplied both top and bottom of the fraction with the Least Common Denominator of a^2*b^2. Then I factored out (b+a) out of both top and bottom of the fraction, leaving the top with ab and the bottom with b-a. Of course, I just may be wrong! 🙂
I hope this helps!
I called her as a follow-up, and it was the right answer. As it turns out, her husband had an uber-calculator that could churn out the answer, but he needed to know *how* to do it, i.e. show the work. Since I learned algebra, trig, and calculus old school — i.e., sans calculator — I still had all of this math info/formulae still floating around in my head while I had *no* experiential memory of using a calculator to, well, calculate. It was still frustrating, though, knowing that solving stuff like above used to be easy as pie and it’s not anymore.
As it turns out, my little sister was in the same quandery, but it’s been even longer since she’s done algebra. But then we spent an hour on the phone, spooging about solving algebraic equations, of all things. “It’s like figuring out a puzzle with numbers,” I said. “Yeah! It’s fun when it’s like that!” she replied.
Wow. We’re nerds. 🙂