12/3/09

Test 10 Section 8 - #15 (page 981)

Holy cow.  Before we do anything else, let's clean this up a bit.  Remember, this is a #15 out of 16, so we often have to do a little legwork before we really get busy.

The first thing you want to do is cancel out that pesky extra n (I'm gonna show you my sloppy handwriting for this one since we're dealing with big fractions).  That'll get you:

Combine everything (note that you don't HAVE to FOIL if you don't want, since we've got the factored version of Difference of Two Squares):

Now, the numerators on either side are basically telling us that n = 5.  Well, then n2 is 25, and [n2 - 1] (our denominator) is 24.   Answer choice C says k is 24, and that's our answer.

Note that this also could technically have been a BACKSOLVE question, although not the easiest one. If you jumped to the answer choices once you simplified you'd start with C, which says k is 24, and you'd figure out what n would have to be to make [n2 - 1] = 24.  So long as your n is an integer (which 5 of course is), you're good to go.

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