Ah, inequality. That terrible, terrible thing. What does one do when confronted with inequality? Well, usually we march, protest, or legislate against it. What do mathematicians do? We work out its domain and range.

So what's stumping me tonight? Well, many things are stumping me tonight, but I feel like I'm getting into my groove. What in particular is stumping me however is this:

So I multiply both sides by the denominator:

Which gives me:

That, my friends, is not a true statement. So what did I do wrong?

If you haven't already, check out the post below this to see the problem I was having. Now, back to me.

My mistake was elementary. With the second term, when distributing the t into the other two, I distributed incorrectly. So we started with this: 

Let's take a look at that second term more closely. First time around I distributed like this: 

But what I should have done was this: 

Let's look at it another way and commute the multiplication in this term. I'll finish the problem after the break. 

More...

Currently in the process of doing prerequisite review for my pre-calculus 7A-7B. Either the review material is more difficult than the stuff I learned in MathPath1, or I've forgotten more than I'd care to admit. Either way, the current problem that has me stumped is as follows:

So, looking at this, my first thought is to multiply both sides by the LCD.

This leaves me with the expression:

Bits divide out nicely, leaving me with:

This multiples out and simplifies to:

And that doesn't factor nicely. Now, I could go to completing the square, but according to the computer, this whole problem is meant to be equivalent to a first-degree linear equation. So, people - what have I missed?

Incidentally, I hate fractions.

Also, elections happened at my college. I took it rather seriously - in fact, probably a bit too seriously, but then democracy, and proper voting, and respect for the voting population matters to me. There was a lot mismanaged about this election, but I think what says it all to me is this:

Last year, 700 students turned out to vote. This year, at least 1200 did. That's awesome. But in Fall 2009, we had 29,709 students enrolled. I don't know if they're all eligible to vote, but let's assume that they are.

To figure out the percentage a number x is of y, you can use a pretty simple formula.  . So, assuming those figures are accurate, and they were all eligible to vote (I couldn't find anything in the bylaws to say that they weren't), that gives us the equation  . So, the voter turnout was 4.04%, assuming that's accurate. It may not be. But even so, out of almost 30,000 students who attend my community college, only 1200 of them voted. It's great that it's better than last year, but it shows that something needs to be done to improve student participation in these elections. And the math proves it.