Algebra II Chapter 8 Part 2: Rational Functions Chapter 8 Lesson 4 Multiply and Divide Rational Functions Vocabulary Words to Review: Reciprocal The rules of fractions DO NOT change! *When adding and subtracting, you will need common denominators! *When multiplying, you will need to multiply straight across! *When dividing, you will need to multiply by the reciprocal! 1
Example 1: Simplify a Rational Expression If something is factorable, FACTOR IT! Remember the x box? Example 3: Standardized Test Practice The rules of fractions DO NOT change! *When multiplying, you will need to multiply straight across! You will need to use your properties of exponents!!!! 2
Example 4: Multiply Rational Expressions The rules of fractions DO NOT change! *When multiplying, you will need to multiply straight across! If something is factorable, FACTOR IT! Remember the x box? Example 5: Multiply a Rational Expression by a Polynomial As always, when multiplying fractions, make sure that you have 2 fractions! 3
Example 6: Divide Rational Expressions The rules of fractions DO NOT change! *When dividing, you will need to multiply by the reciprocal! *AKA: Same, Change, Flip or Copy Dot Flop Example 7: Divide a Rational Expression by a Polynomial As always, when dividing fractions, make sure that you have 2 fractions! Then, multiply by the reciprocal! 4
Example 2: Solve a Multi Step Problem Chapter 8 Lesson 5 Add and Subtract Rational Expressions Vocabulary 5
Example 1: Add or Subtract with Like Denominators The rules of fractions DO NOT change! *When adding and subtracting, you will need common denominators! Example 2: Find a Least Common Multiple (LCM) Finding LCM: 1. Factor the polynomials. 2. Rewrite all monomials as a product of primes. 3. Look for commonalities. Remember that the common pieces will only need to be represented once in the least common multiple. 4. Make sure to "combine" the rest of the factors so that all factors are represented. 6
Example 3: Add with Unlike Denominators The rules of fractions DO NOT change! *When adding and subtracting, you will need common denominators! Finding LCM: 1. Factor the polynomials. 2. Rewrite all monomials as a product of primes. 3. Look for commonalities. Remember that the common pieces will only need to be represented once in the least common multiple. 4. Make sure to "combine" the rest of the factors so that all factors are represented. Example 4: Subtract with Unlike Denominators Don't forget to distribute the negative!!!! The rules of fractions DO NOT change! *When adding and subtracting, you will need common denominators! Finding LCM: 1. Factor the polynomials. 2. Rewrite all monomials as a product of primes. 3. Look for commonalities. Remember that the common pieces will only need to be represented once in the least common multiple. 4. Make sure to "combine" the rest of the factors so that all factors are represented. 7
Example 5: Simplify a Complex Fraction (Method 1) Example 6: Simplify a Complex Fraction (Method 2) Finding LCM: 1. Factor the polynomials. 2. Rewrite all monomials as a product of primes. 3. Look for commonalities. Remember that the common pieces will only need to be represented once in the least common multiple. 4. Make sure to "combine" the rest of the factors so that all factors are represented. 8
Chapter 8 Lesson 6 Solve Rational Equations Vocabulary Words to Review: Extraneous Solution Example 1: Solve a Rational Equation by Cross Multiplying 9
Example 2: Write and Use a Rational Model Example 3: Standardized Test Practice 10
Example 4: Solve a Rational Equation with Two Solutions 1. Find the common denominator. 2. Apply it to all terms. 3. Multiply both sides by the denominator. (Notice that you are only left with the numerator values! :) ) 4. Solve for x. If it is a subtraction problem, don't forget to distribute the negative! Example 5: Check for Extraneous Solutions 1. Find the common denominator. 2. Apply it to all terms. 3. Multiply both sides by the denominator. (Notice that you are only left with the numerator values! :) ) 4. Solve for x. If it is a subtraction problem, don't forget to distribute the negative! 11
Example 6: Solve a Rational Equation Given a Function NOTE: When entering polynomials as the numerator or denominator of a fraction, ALWAYS use parentheses around the polynomial! 12