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Algebra

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

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Algebra

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  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. 2x 3 3x + 1 A rational expression is undefined when the denominator is equal to zero. x2 – 9 x + 4 x2 + 1 What values of x will make each expression undefined? 2 16 8(2) = = ***Simplifying a fraction is actually factoring then canceling!! 40 8(5) 5 ***A rational expression is simplified when the largest common factor of each the numerator and denominator is cancelled!

  3. Simplify 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! • 15 – 5x • 5x 5(3 – x) 5(x) 3 – x x = = A common mistake… NOOOOO!!!!! 2) 2x2 x2 + 5x x(2x) x(x+ 5) 2x x+ 5 = = NOOOOO!!!!! 3) 5x + 3 x+ 3 5x + 3 x+ 3 = The rational expression is already simplified!

  4. Simplify Let’s Try One! • 2x2 – 6x • 6x2 x – 3 3x 2x(x – 3) 2x(3x) = = You Try One! 2) 15x 5 – 10x 3x 1 – 2x 5(3x) 5(1 – 2x) = =

  5. Recognizing Opposite Factors.Check this out! Simplify. (2 – x) cannot cancel with (x – 2) If you recognize opposites. Factor out a -1. (2 – x) = -1( ) x – 2 Watch This One! DTS • 4 – x2 • x2 – x – 2 -1(x – 2)(x + 2) (x – 2)(x + 1) (2 – x)(2 + x) x + 2 x + 1 = = = (x – 2)(x + 1) Try One Together! 2) x2 + 6x + 9 9 – x2 (x + 3)2 x + 3 3 – x = = (3 – x)(3 + x) DTS Try One On Your Own! 5 – x 3) 5 – x x2 – 8x + 15 -1(x – 5) (x – 5)(x – 3) 1 x – 3 1 3 – x = = = = (x – 5)(x – 3)

  6. For what values of x is the rational expression undefined? Basically, find the value(s) of x that make the denominator 0! Similar to the zero-product property! • 15 – 5x • 5x + 3 x = -3/5 2) 2x2 x2 – 16 x = 4, -4 DTS (x + 4)(x – 4) 3) 5x + 3 x2 + 3x + 2 x = -1, -2 (x + 2)(x + 1)

  7. One from the HW • P. 668 #30

  8. HW • P. 667  #9-31,  42-49

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