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Unit 7: Rational Functions

Unit 7: Rational Functions. Multiplying & Dividing Rational Expressions. Simplifying Rational Expressions. Things to look for: Can numerator &/or denominator be factored? Can any factors be divided out (cancelled)?

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Unit 7: Rational Functions

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  1. Unit 7: Rational Functions Multiplying & Dividing Rational Expressions

  2. Simplifying Rational Expressions • Things to look for: • Can numerator &/or denominator be factored? • Can any factors be divided out (cancelled)? • For what values of x (if any) will the expression be undefined? (i.e. are there any values of x that will make the denominator = 0) • Things to remember: • Exponential properties from Algebra 1. • Individual terms of polynomial expressions (i.e. anything separated by a + or -) CANNOT be divided out/reduced/cancelled. (“If you can’t simplify EVERYTHING, you can’t simplify ANYTHING”) • Most importantly: no self-respecting math teacher, textbook, or Accuplacer writer will ask you to simplify a rational expression unless SOMETHING can be factored & divided out!

  3. Simplifying Rational Expressions Rewrite numerator in standard form & factor out –x (remember we don’t like leading coefficients to be negative). Factor the denominator. Once everything is factored, identify values of x that would make the expression undefined (in this case 2 & -1). Then simplify/cancel. From the previous step, we know the zeros of the denominator are 2 & -1. Thus, the expression is undefined at those values; we can say the expression has a domain of x ≠ 2 or x ≠ -1.

  4. Multiplying/Dividing Rational Expressions • REMEMBER: Rational expressions are fractions; multiply/divide them using the same rules. • Things to do BEFORE multiplying: • Factor all numerators & denominators. • Divide out any common factors. • After multiplying across, be sure final numerator & denominator cannot be simplified further.

  5. Multiplying/Dividing Rational Expressions (assume all expressions are defined) It looks scary now, but wait until we factor. First, flip the second fraction (property of division). Both denominators are differences of squares; factor them. We can also factor out a 4 from the 2ndnumerator. Factor the numerators (you will probably need to do some side work). Now look at all the stuff that will cancel! (Remember that “self-respecting math teacher” thing?)

  6. Multiplying/Dividing Rational Expressions (assume all expressions are defined) Not so scary now, is it? Multiply across & we’re done! You can distribute in the numerator if you want. Usually we let the answer choices (Quest, Accuplacer, etc.) dictate whether that’s necessary.

  7. Journal Entry • TITLE: Rational Expressions 3-2-1 • Identify 3 things you already knew from this presentation. • Identify 2 new things you learned from this presentation. • Identify 1 question you still have about this presentation.

  8. Homework Quest: Multiplying & Dividing Rational Expressions Due 2/8 (A-day) or 2/9 (B-day)

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