Picture The Youth as Those Doing Their Precalculus Homework While I'm Here Typing All This or, A Test Post to Set The Tone for The Rest of This Blog

Solution to problem 11 on page 253:

The quantity of x minus three all over x, minus three over the quantity of x plus one, plus 3 over the quantity of x squared plus x equals zero. Multiply all of this by the least common denominator (i.e. the quantity of x plus one, all times x). You 'll get the quantity of x minus three times the quantity of x plus one, minus three x, plus three, which is all equal to zero. Once you multiply out the two binomials, the negative three and the positive three cancel, leaving you with (once you add like terms) x squared minus five x (which equals, again, zero). You can factor an x out of this, making it x times the quantity of x minus five (zero). Some intuitive steps can be omitted here, but they involve setting both x and x minus five equal to zero and then solving for two different values of x. You'll end up with x equaling zero and x equaling 5. But if you look back at the original equation, you'll see that x cannot equal zero because x is a denominator in the original equation. Since a function can never be legit with an x in the denominator, zero is an extraneous root, which leaves 5 as the only possible value of x.<sup>1

1</sup> This is what I'm pretty sure is the best way to illustrate how I think the youth looked at the article about the whole snow day/superintendent's wife/Facebook thing (i.e. "Or, for something so obvious to the limit, you could say it in a way that's tons more appropriately efficient...").