1. Rational Algebraic Expressions
Objective: To simplify rational algebraic expressions

2. Rational Algebraic Expression
Quotient of two algebraic expressions
Example:

3. Simplify the following expression:
start by factoring
after the polynomials are factored you can “cancel” terms whose quotient is one

4. Finding domain and zero’s
Given:
Start by factoring the numerator and denominator.
The domain of the function is all reals except where the denominator equals zero x ≠ 0 x + 2 ≠ 0 x – 2 ≠ 0 x ≠ 0 x ≠ -2 x ≠ 2

5. Zeros of the function
The zeros of the function are where the numerator equals zero.
2x + 1 = 0 x – 2 = 0 x = -½ x = 2
Remember x = 2 is not in the domain so it cannot be a zero of the function.

6. Try These! Simplify 2x – 1 More try these!
#5 Hint: add and subtract all missing terms

7. Back to Try These!

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12. Try These! Find the domain and zeros of the function
D: x ≠ 0, x ≠ -4 zeros {2, -2}
D: x ≠ -1/3 x ≠ -4 zeros {-3/2, -2}
D: x ≠ -1 zeros {-2}