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01 Simplifying Rational Expressions.notebook March 05, 2015 Homework Worksheet 15-1 Pick a career to research for your paper!! Vocabulary Rational Number A fancy way of saying "fraction" Expression An algebraic expression that has a variable and NO equal sign Rational Expression An algebraic fraction 1 01 Simplifying Rational Expressions.notebook March 05, 2015 Simplify 1. 2. 3. What about: ? How does relate to factoring? So, by factoring the numerator, we were able to cancel a factor from the numerator with the denominator. 2 01 Simplifying Rational Expressions.notebook March 05, 2015 Steps for Simplifying Rational Expressions: 1. Factor the Numerator Factor the Denominator 2. Find all excluded values for the denominator. (ie: Values that make the denom zero) 3. Cancel like factors (ie: Factors in num w/factors in denom) 4. Rewrite expression Notes: 1. Factor the ENTIRE polynomial - NOT numbers. 2. "Excluded Values" are the numbers that make the values in the ( ) in the denominator zero. 3. Only things that are being MULTIPLIED may be canceled. 4. NEVER, EVER CANCEL PARTS OF SUMS!!! (This is the ultimate sin in mathematics!!) 3 01 Simplifying Rational Expressions.notebook March 05, 2015 A sum is any two terms connected with a "+" sign or a "-" sign in between them. x + 5 x Part of the sum is: The other "part" is: 5 How do you know? x & 5 are the 2 terms attached by a "+" The Golden Rule of Algebra: You can NEVER EVER cancel parts of sums!! In The Example: x + 5 To NEVER EVER cancel parts of sums means: You cannot cancel the "x" part or the "5" part, unless you cancel the entire "x + 5" part!! 4 01 Simplifying Rational Expressions.notebook March 05, 2015 Examples: because the "5" in the numerator is part of the sum "x+5" and cannot be canceled with the 25 in the denominator. because the 15 & y in the numerator is NOT a sum, they are parts of a product (multiplication) which CAN be canceled with the 3 & y in the denominator. Sums or Products? 1. x + 3 "+" --> Sum 3. 2x No "+" --> Product 2. 2x + 6 "+" --> Sum 4. 6 – x "-" --> Sum 5 01 Simplifying Rational Expressions.notebook March 05, 2015 Steps for Simplifying Rational Expressions: 1. Factor the Numerator Factor the Denominator 2. Find all excluded values for the denominator (ie: Values that make the ( ) in the denom zero) 3. Cancel like factors (ie: Factors in num w/factors in denom) 4. Rewrite expression Simplify completely (if possible) and state excluded values 1. 2. 6 01 Simplifying Rational Expressions.notebook March 05, 2015 Simplify completely (if possible) and state excluded values 3. 4. Simplify completely (if possible) and state excluded values 5. 6. 7 01 Simplifying Rational Expressions.notebook March 05, 2015 Simplify completely (if possible) and state excluded values 7. 8. Simplify completely (if possible) and state excluded values 9. 10. 8