Math-1010 Lesson 4-2. Add and Subtract Rational Expressions

Transcription

1 Math-00 Lesson - Add and Subtract Rational Epressions

2 What are like terms? Like variables: Like powers: y y Multiples of the same variable same base and same eponent. Like radicals: same radicand and same inde number. Like fractions:, same denominator.,

3 Adding Fractions We can add like fractions Combine the numerator over a common denominator. 7

4 Least Common Multiple: The smallest number that two other numbers divide evenly. Used for: Obtaining Least Common Denominators: Both denominators have a common factor of 6. Left denominator has an uncommon factor of Multiply by one in the form of right denominator has an uncommon factor of 7 Multiply 0 by one in the form of 7 7

5 Vocabulary A rational number can be written as a ratio of integers., A rational epression can be written as a ratio of epressions. ( ) We will be looking at ratios of polynomial epressions. Ecluded Value: the value for that results in division by zero ( ),

6 What type of rational epressions can you combine together using addition or subtraction? like rational epressions Which of these epressions are like epressions?. ( ). ( ). ( ). ( ) Which of these epressions are like epressions?. ( )( ) 6. ( ) ( )

7 . ( What is the ecluded value for each epression? ). ( )( ) 6. ( ). ( ).. ( ) 7 8. ( ),. ( ),

8 Simplifying Fractions What property are you applying? Identity Property Of Multiplication 8 multiplying by in the form of ¼ over ¼ Unfortunately this method WILL NOT WORK for simplification of ratios of polynomials.

9 Simplifying Fractions You must FACTOR the fractions Break them apart into the product of fractions. Notice the fractions that equal 8

10 Simplifying Fractions You must FACTOR the fractions Break them apart into the product of fractions. Notice the fractions that equal 8 ( ( ( )( ) ( )( ) ) ( ) ( ( ( ) ) ) ) ( ) ( )

11 Adding/Subtraction Rational Epressions The easy problem: Combine the numerator over a common denominator. The easy problem: Can you combine and? 7 7 ( ) ( ) ( ) Why not? 7 Combine the numerator over a common denominator. 7

12 Your turn: add/subtract ( ) ( ) Can you do it this way? What property are we using? Inverse Property of Multiplication. () Why not? You CANNOT use the Inverse Property of Multiplication on addends.

13 Your turn: add/subtract ( ) I will not allow you to simplify using the Inverse Property of Multiplication until you have factored it into two fractions. ( ) ( ) Only then will you be able to see how the Inverse Property of Multiplication changes the rational epression into multiplication by one.

14 ( Your turn: add/subtract 7) ( 7) ( ( ) Which one is correct? ) 7 Subtract every term in the right side numerator! (Half of you will make this mistake on the HW and on the Test). 7 Can you factor this into two fractions multiplied together?

15 No common denominator. ( ) ( ) Multiply the left side fraction by one in the form of / Multiply the right side fraction by one in the form of / ( ) + ( ) ( ) ( ) ( ) ( ) Can you factor this into two fractions multiplied together?

16 Your turn: simplify 6 ( ) ( ) ( ) 6 6 6

17 Your turn: simplify ( ) ( ) ( ) ( ) ( ) ( 6) ( ) ( 6) Can you factor this into two fractions multiplied together?

18 Your turn: simplify ( ) ( 0 ) 0 ( ) Can you factor this into two fractions multiplied together?

19 What is the factored version of the left denominator? ( 8)( ) ( ) What is the least common denominator? ( 8)( ) (step by step)

20 Your Turn: add the two rational epressions ( 8)( ) ( ) ( 8)( ) ( ) ( ( 8) 8) ( 8) ( 8)( ) ( 8)( ) ( 6 8)( ) ( ) ( 8)( ) Can you factor this into two fractions multiplied together?

21 Your Turn: simplify ) ( ) )( ( ) (

22 Simplify the comple fraction. 6 6 Fraction: numerator denominator Vocabulary: Division: Division by a number is the same thing as Multiplication by the reciprocal of the number

23 Vocabulary Comple Fraction is a fraction in the numerator and a fraction in the denominator. How do you divide fractions? Multiply by reciprocal. Simplifying comple fractions: 6

24 A more complicated Comple Fraction ( ( ) ) ( ( ) ) Put binomials into parentheses!

25 Your turn: Simplify the comple fraction. ) ( ) (

26 Sum/difference in Numerator and Denominator. Combine the numerator fractions into one fraction. 6 = 6 = 8. Combine the denominator fractions into one fraction. 8 8 = ( 8) ( )

27 Your turn: Simplify the comple fraction.