1. Algebra 11.4 Simplifying Rational Expressions (This information will be on the STAR Test!)

2. Rational Expressions Do you remember the definition of a rational number? Any number that can be written as the quotient of two integers: ½, 7/4, 5 etc. Rational Expression: a fraction whose numerator, denominator, or both are nonzero polynomials. 3x + 13 2x x + 4 x 2 – 9 x 2 + 1 A rational expression is undefined when the denominator is equal to zero. What values of x will make each expression undefined? ***Simplifying a fraction is actually factoring then canceling!! 16 40 8(2) 8(5) == 2 5 ***A rational expression is simplified when the largest common factor of each the numerator and denominator is cancelled!

3. Simplify 1)15 – 5x 5x Do not cancel terms unless they are common factors of the numerator and denominator!!! = 5x is not a factor of all terms, therefore you cannot cancel 5x! 2) 2x 2 x 2 + 5x 5(3 – x) 5(x) = 3 – x x NOOOOO!!!!! = x(2x) x(x + 5) 2x x + 5 = 3) 5x + 3 x + 3 NOOOOO!!!!! = The rational expression is already simplified! 5x + 3 x + 3 A common mistake…

4. Simplify Let’s Try One! 1)2x 2 – 6x 6x 2 2x(x – 3) 2x(3x) x – 3 3x == You Try One! 2) 15x 5 – 10x 5(3x) 5(1 – 2x) 3x 1 – 2x ==

5. Recognizing Opposite Factors. Check this out! Simplify. Watch This One! 1) 4 – x 2 x 2 – x – 2 (2 – x)(2 + x) -1(x – 2)(x + 2) (x – 2)(x + 1) == DTS (x – 2)(x + 1) (2 – x) cannot cancel with (x – 2) If you recognize opposites. Factor out a -1. (2 – x) = -1( ) x – 2 x + 2 x + 1 = Try One Together! 2) x 2 + 6x + 9 9 – x 2 (x + 3) 2 = DTS (3 – x)(3 + x) x + 3 3 – x = Try One On Your Own! 3) 5 – x x 2 – 8x + 15 (x – 5)(x – 3) -1(x – 5) (x – 5)(x – 3) == 1 x – 3 = 5 – x 1 3 – x =

6. For what values of x is the rational expression undefined? 1)15 – 5x 5x + 3 2) 2x 2 x 2 – 16 3) 5x + 3 x 2 + 3x + 2 Basically, find the value(s) of x that make the denominator 0! Similar to the zero-product property! x = -3/5 DTS (x + 4)(x – 4) x = 4, -4 (x + 2)(x + 1) x = -1, -2

7. One from the HW P. 668 #30 P. 668 #30

8. HW P. 667 #9-31, 42-49 P. 667 #9-31, 42-49