Algebra Algebra Algebra

I don't know why I'm surprised. I knew that from teaching calculus a long time ago, that it always seemed to be the pesky algebra that mostly tripped kids up. I guess I thought it would be different with my current crop of precalculus kids. They're different, I told myself. They're more savvy, I said. They won't have the standard problems, I lied to me. No. They're not and not and they will. And I hesitate to say "algebra". More like "simplifying rational expressions". We're going over algebraic manipulations of limits, and I gave them basic polynomials and basic "single numerator / single denominator" expressions. They did fine. They were all impressed with themselves that they could chat up limits like they owned the place. And then WHOA. We delved into fractions imbedded in fractions. Huh! What do you mean I have one over "w+4" minus 1/4 ALL over w? What would I do with that? What? Common denom whozits? Oh! So to get the common denominator of "1 over 'w+4'" and "1/4", I can just add 4 to the top and bottom of 1/4! Who knew! Or! Once I get that sorted out, when I then have to simplify dividing by w ...... oh! I can just bring it to the "top" and multiply by w, right? Oy! And in another problem, the numerator was "9 - v" and the denominator was "(v - 9)(.......)". The student didn't see the connection of how to easily and correctly manipulate the two. It seemed like cheating to her when I mentioned how. I guess it's a never-ending refreshing of their memory and of practicing and going over concepts. They're so used to JUST dealing with fractions involving ONLY numbers that this may have been too much of a leap for them. Now I'm debating whether to delve into derivatives or to just sprinkle in more intensive algebra and unit circle refreshers in hopes that they'll have an easier time next year in calculus.