G8 Math Q1- Week 3- Simplifying Rational Expression.pptx

mathematics 8

1. SIMPLI FYING RAT IONAL EXPRES SIONS

2. RATIONAL EXPRESSIONS Rational expressions can be written in the form where P and Q are both polynomials and Q 0. Examples of Rational Ex pressions P Q 3 x 2 2 x 4 4 x 3 y 3 x 2 4 x 5 2 x 2 3 xy 4 y 2 4

3. Simplifying Rational Expressions The process of simplifying numbers is the same with simplifying rational expressions.

4. GROUP ACTIVITY Di rections: Analyze the following numbers whether a Rational Expression or Rational N umbers. You only have 5 minutes for this acti vity.

5. • 2/-3 • 2x 2 +7x/x + 1 • -1/5 • 6x/6 • 9x 2 -1/4x 2 + 5 • 25/3x • 10x 2 +4x + 9/ x 2 + 4 • 8/5 • 1 • • X 2 + 4x + 4/ x 2 – 1 • 2x + 10/ x + 5 • 2x + 8/ 3x + 12 • 1/ x • 2/3

6. Correct Answer RATIONAL NUMBERS 1. 2 /-3 2. - 1/5 3. 8/5 4. 2/3 RATI ONAL EXP RESSION 1.2x 2 +7x/x + 1 2. 9x 2 -1/4x 2 + 5 3.10x 2 +4x + 9/ x 2 + 4 4.X 2 + 4x + 4/ x 2 – 1 5.X 2 + 4x + 4/ x 2 – 1 6.2x + 10/ x + 5 7.2x + 8/ 3x + 12

7. SI MPLIFY: 1. X – 1 5x - 5 Solutio ns: = (x – 1) 5( x – 1) = (x – 1) 5( x – 1) Final answer: 1 5 STEP S: 1. Look for the GCF or the common factor of the numerator and d enominator. 2. Cancel the common fac tor.

8. SIMPLIFY THE EXPRESSION 2. xy + 3y 4x + 12 Solut ion: = y ( x + 3) 4 ( x + 3) = y ( x + 3) 4 ( x + 3) Final Answer: y 4 Ste ps: 1. Look for the GCF or the common factor of the numerator and d enominator. 2. Cancel the common fac tor.

9. YOUR TURN! GROUP 1: 4b + 8a GROUP 4: bc + 2ac 2x + 8 3x + 12 GROUP 2: 2xy + 4y 2 x 2 + 2xy GROUP 3: 2x + 10 x + 5

10. Simplifying Rational Expressions Simplifying a rational expression means writing it in lowest terms or simplest form. To do this, we need to use the Fundamental Principle of Rational Expressions If P , Q , and R are polynomials, and Q and R are not 0, PR QR P Q

11. Simplifying a Rational Expression 1) Completely factor the numerator and den ominator. 2) Apply the Fundamental Principle of Rational Expressions to eliminate common factors in the numerator and denominator. Warnin g! Only common FACTORS can be eliminated from the numerator and denominator. Make sure any expression you eliminate is a facto r.

12. Example 2: Simplifying Rational Expressions Simplify each rational expression, if possible. Identify any excluded value s. Factor 14. Divide out common factors. Note that if r = 0, the expression is undefine d. Simplify. The excluded value is 0.

13. Ex ample Simplify the following expression. 7 x 35 7 ( x 5 ) 7 x 2 5 x x ( x 5 ) x

14. Ex ample Simplify the following expression. x 2 3 x 4 ( x 4)( x 1) x 1 x 2 x 20 ( x 5)( x 4) x 5

15. Ex ample Simplify the following expression. 7 y y 7 1 ( y y 7 7 ) 1

16. Simplify each expression. 1. 2 . Factor each expression. 3. x 2 + 5 x + 6 4. 4 x 2 – 64 ( x + 2)( x + 3) 5. 2 x 2 + 3 x + 1 (2 x + 1)( x + 1) 4( x + 4)( x – 4) 6. 9 x 2 + 60 x + 100 (3 x +10) 2

17. GENER ALIZATION What is Rational Expres sion? What is Rational Nu mbers? What are the steps in simplifying rational expre ssion?

18. INDIVIDUAL SEATWORK • Get ½ crosswise. Direction: Simplify the following expression 1. 5x 2 + 20 2x + 8 2. 21xy + 6y 2 42x + 12y 3.2x 2 + 2x 3x 2 + 3x 4. x – 1 x 2 – 1 5. p 2 – p -6 p - 3

19. CORRECT ANSWER 1. 5 /2 2.3y/6 or y/2 3. 2x /3x 4.1/x + 1 5. p + 2/ 1

20. CORRECT ANSWER 1. 5 /2 2.3y/6 or y/2 3. 2x /3x 4.1/x + 1 5. p + 2/ 1