Math-00 Lesson - Add and Subtract Rational Epressions
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.,
Adding Fractions We can add like fractions Combine the numerator over a common denominator. 7
Least Common Multiple: The smallest number that two other numbers divide evenly. Used for: Obtaining Least Common Denominators: 0 6 67 6 7 7 67 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
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 ( ),
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 8. ( )
. ( What is the ecluded value for each epression? ). ( )( ) 6. ( ). ( ).. ( ) 7 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.
Simplifying Fractions You must FACTOR the fractions. 8 8 8 Break them apart into the product of fractions. Notice the fractions that equal 8
Simplifying Fractions You must FACTOR the fractions. 8 8 8 Break them apart into the product of fractions. Notice the fractions that equal 8 ( ( ( )( ) ( )( ) ) ( ) ( ( ( ) ) ) ) ( ) ( )
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
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.
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.
( 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?
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 / ( ) + ( ) ( ) ( ) ( ) ( ) 6 6 6 8 7 6 Can you factor this into two fractions multiplied together?
Your turn: simplify 6 ( ) ( ) 6 6 6 ( ) 6 6 6
Your turn: simplify ( ) ( ) ( ) ( ) ( ) ( 6) ( ) ( 6) Can you factor this into two fractions multiplied together?
Your turn: simplify ( ) ( 0 ) 0 ( ) 0 0 0 Can you factor this into two fractions multiplied together?
What is the factored version of the left denominator? ( 8)( ) ( ) What is the least common denominator? ( 8)( ) (step by step)
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?
Your Turn: simplify ) ( ) )( ( ) (
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. 6 6 6
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
A more complicated Comple Fraction ( ( ) ) ( ( ) ) Put binomials into parentheses!
Your turn: Simplify the comple fraction. ) ( ) (
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) ( )
Your turn: Simplify the comple fraction.