1. §6.3 Complex Rational Fcns
Chabot Mathematics
§6.3 Complex Rational Fcns
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer

2. 6.2 Review § Any QUESTIONS About Any QUESTIONS About HomeWork
MTH 55
Review §
Any QUESTIONS About
§6.2 → Add-n-Sub Rational Expressions
Any QUESTIONS About HomeWork
§6.2 → HW-19

3. 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. Simplify Complex Rational Expressions by Dividing
Add or subtract, as needed, to get a single rational expression in the numerator.
Add or subtract, as needed, to get a single rational expression in the denominator.
Divide the numerator by the denominator (invert and multiply).
If possible, simplify by removing any factors equal to 1

5. 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. 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. Solution cont.
Rewriting with a division symbol. This is often done mentally.
Multiplying by the reciprocal of the divisor (inverting and multiplying)

8. Example  Simplify
SOLUTION Write the numerator and denominator as equivalent fractions.

9. Simplify Complex Rational Expressions by LCD Mult.
Find the LCD of ALL rational expressions within the complex rational expression.
Multiply the complex rational expression by a factor equal to 1. Write 1 as the LCD over itself (LCD/LCD).
Simplify. No fractional expressions should remain within the complex rational expression.
Factor and, if possible, simplify.

10. Example  Simplify
SOLUTION - In This Case look for the LCD of all four factors.
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. Solution cont.
Using the distributive law
Simplifying

12. Example  Simplify SOLUTION - The LCD 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. Example  Simplify SOLUTION
The LCD is x3 so we multiply by 1 using x3/x3.
Using the distributive law
All fractions have been cleared and simplified.

14. Example  Simplify
SOLUTION: Multiply the numerator and denominator by the LCD of all the rational expressions; 2x here

15. Example  Simplify SOLUTION: Multiplying by 1, using the LCD.
Multiplying the numerator and the denominator. Remember to use parentheses.

16. Example  Simplify SOLN cont.
Using the distributive law to carry out the multiplications
SOLN cont.
Removing factors that equal 1. Study this carefully. Take CARE with CANCELLING
Simplifying
Factoring. This does not simplify further

17. Example  Simplify SOLUTION: Rewrite using only positive exponents
LCD of all individual Rational Expressions is x3y3
Simplified Version is still a bit “Complex”

18. WhiteBoard Work Problems From §6.3 Exercise Set
38, 42, 48, 53
Three Resistors in Parallel

19. All Done for Today
Liquid Crystal Display
More Info on LCDs

20. Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu
Chabot Mathematics
Appendix
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer –

21. Graph y = |x|
Make T-table