1. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 1 Bruce Mayer, PE Chabot College Mathematics Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Chabot Mathematics §6.3 Complex Rational Fcns

2. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 2 Bruce Mayer, PE Chabot College Mathematics Review §  Any QUESTIONS About §6.2 → Add-n-Sub Rational Expressions  Any QUESTIONS About HomeWork §6.2 → HW-24 6.2 MTH 55

3. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 3 Bruce Mayer, PE Chabot College Mathematics Complex Rational Expression  Complex Rational Expression is a rational expression that contains rational expressions within its numerator and/or its denominator.  Some examples: The rational expressions within each complex rational expression are red.

4. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 4 Bruce Mayer, PE Chabot College Mathematics Simplify Complex Rational Expressions by Dividing 1.Add or subtract, as needed, to get a single rational expression in the numerator. 2.Add or subtract, as needed, to get a single rational expression in the denominator. 3.Divide the numerator by the denominator (invert and multiply). 4.If possible, simplify by removing any factors equal to 1

5. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 5 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLUTION Rewriting with a division symbol Multiplying by the reciprocal of the divisor (inverting and multiplying) Factoring and removing a factor equal to 1.

6. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 6 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLUTION Multiplying by 1 to get the LCD, 3, for the numerator. Multiplying by 1 to get the LCD, 2x, for the denominator. Adding Subtracting

7. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 7 Bruce Mayer, PE Chabot College Mathematics Solution cont. Rewriting with a division symbol. This is often done mentally. Multiplying by the reciprocal of the divisor (inverting and multiplying)

8. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 8 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLUTION Write the numerator and denominator as equivalent fractions.

9. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 9 Bruce Mayer, PE Chabot College Mathematics Simplify Complex Rational Expressions by LCD Mult. 1.Find the LCD of ALL rational expressions within the complex rational expression. 2.Multiply the complex rational expression by a factor equal to 1. Write 1 as the LCD over itself (LCD/LCD). 3.Simplify. No fractional expressions should remain within the complex rational expression. 4.Factor and, if possible, simplify.

10. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 10 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLUTION - In This Case look for the LCD of all four Terms. Multiplying by a factor equal to 1, using the LCD: 12/12=1 Multiplying the numerator by 12 Don’t forget the parentheses! Multiplying the denominator by 12

11. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 11 Bruce Mayer, PE Chabot College Mathematics Solution cont. Using the distributive law Simplifying

12. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 12 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLUTION - The LCD for all is x Using the distributive law  When we multiply by x, all fractions in the numerator and denominator of the complex rational expression are cleared:

13. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 13 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLUTION The LCD for all is x 3 so we multiply by 1 using x 3 /x 3. Using the distributive law All fractions have been cleared and simplified.

14. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 14 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLUTION: Multiply the numerator and denominator by the LCD of all the rational expressions; 2x here

15. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 15 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLUTION: Multiplying by 1, using the LCD. Multiplying the numerator and the denominator. Remember to use parentheses.

16. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 16 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLN cont. Using the distributive law to carry out the multiplications Removing factors that equal 1. Study this carefully. Take CARE with CANCELLING Simplifying Factoring. This does not simplify further

17. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 17 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLUTION: Rewrite using only positive exponents LCD of all individual Rational Expressions is x 3 y 3 Simplified Version is still a bit “Complex”

18. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 18 Bruce Mayer, PE Chabot College Mathematics WhiteBoard Work  Problems From §6.3 Exercise Set 38, 42, 48, 53  Three Resistors in Parallel

19. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 19 Bruce Mayer, PE Chabot College Mathematics All Done for Today More Info on LCDs  Liquid Crystal Display

20. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 20 Bruce Mayer, PE Chabot College Mathematics Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Chabot Mathematics Appendix –

21. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 21 Bruce Mayer, PE Chabot College Mathematics Graph y = |x|  Make T-table

22. BMayer@ChabotCollege.edu MTH55_Lec-31_sec_6-3_Complex_Rationals.ppt 22 Bruce Mayer, PE Chabot College Mathematics