Day 9, Mat119: Pre-Calculus

Last time: Discussion of problems, section 3.1

Next time: Discussion of problems, section 3.2

Today:

Announcements
- You've got a homework due today (pp. 205--).
- A homework is returned (graded #6, 14, 21, 22). You're having some terrible problems with
  - domains (ask yourself "which parts are causing trouble for x?)
  - algebra, generally. There are lots of strange simplifications of quotients flying around. I'll give you a couple of examples: in problem #6 we started with
    
    ${\frac{x^2+2x}{3x^2-1}}$
    From there, I saw the following:
    
    ${\frac{x^2+2x}{3x^2-1}}$ is not equal to ${\frac{1}{3}x^2+2x-1}$
    
    ${\frac{x^2+2x}{3x^2-1}}$ is not equal to ${\frac{0+2x}{3-1}}$ or ${\frac{1+2x}{3-1}}$
    (Cancelling the ${x^2}$ ).
    
    ${\frac{x^2+2x}{3x^2-1}}$ is not equal to ${\frac{x}{x^2-1}}$
    (Cancelling one term of ${x^2}$ , then cancelling the 2s).
    
    ${\frac{x^2+2x}{3x^2-1}\ne{x^2+2x/3x^2-1}$ which is not equal to ${x^2+2/3x-2}$
  Note that there are two square roots (important for #6, the quotient).
Questions about Models?
Let's do a few more practical problems from that sections....
Our new word for the day:

Polynomials

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${\frac{x^2+2x}{3x^2-1}}$	is not equal to	${\frac{1}{3}x^2+2x-1}$
${\frac{x^2+2x}{3x^2-1}}$	is not equal to	${\frac{0+2x}{3-1}}$ or ${\frac{1+2x}{3-1}}$ (Cancelling the ${x^2}$ ).
${\frac{x^2+2x}{3x^2-1}}$	is not equal to	${\frac{x}{x^2-1}}$ (Cancelling one term of ${x^2}$ , then cancelling the 2s).
${\frac{x^2+2x}{3x^2-1}\ne{x^2+2x/3x^2-1}$	which is not equal to	${x^2+2/3x-2}$