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UNIT 11 Rational Expressions 9-4 Simplifying Rational Expressions Simplest Form: means all terms are completely factored and any common terms are reduced. (there should be no factorable polynomials remaining) Examples: 1) 3x 2 3x 3 21x 2) x2 4 x 2 3) x 2 3x 2 x 2 x 6 4) x 2 x 6 x 2 9 2) 4x 2 4x x 2 x 6 x 2 2x 3 4x Multiply Rational Expressions: Examples: 1) 5x 2 y 6x 3 y 2 2xy 3 10 y x 2 x 2 3x 12 2 3) 3x 2 x 6x 8 Divide Rational Expressions: Examples: 1) 2x 2 x 2 2x 2 3 x 12 x 6 x 8 3) 3) (2 x 2) x 2 3x 2 ( x 1) 4x 2 4x 2 9 x 5 9-5 Add & Subtract Rational Expressions Examples: 1) 3) 7 5 6x 8x 4 3x 2 x 5 7x 14 x 21 2) 3 5 x 3 x 2 4) 2 x 5 x 2 3 x 2 5) 10 x 4 5 2 3x 3 x 1 6x Complex Fractions: EX 1: 1 3 x 5 4 y 2 3 x y EX 3: 5 7 x y EX 2: 3 5 y x UNIT 11 9-6 Rational Equations & Graphs Part 2 Solve Rational Equations Examples: 1) 7 x x 3 4 2) 3) 5x 10 7 x 2 x 2 4) 5) 2 x 5 7 3 x 3x 12 2 2 x 1 x 1 2 3 6 2 x 10 x 2 x 12 x 20 Application: 1) If one student can complete the decorations for the prom in 5 days working alone, another student could do it in 3 days, and a third could do it in 4 days, how long would it take them working together? 2) A round trip flight took 3.9 h flying time. The plane traveled the 510 mi to the city at 255 mi/h with no wind. How strong was the wind on the return flight? Was the wind a head wind or a tail wind? 9-3 Graphs of Rational Functions Examples: Determine any horizontal or vertical asymptotes 1) 1 x 5 2) 3 x 3 30 2x 3 3) 4x 2 x 3 x 2 2x