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# Rational expressions and equations

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### Rational expressions and equations

1. 1. Rational Expressions and Equations Chapter 9 pg 470
2. 2. Review of Rational Expressions <ul><li>A rational expression is an expression that is the quotient of two polynomials. </li></ul><ul><li>Examples include </li></ul>
3. 3. Domain of a Rational Expression <ul><li>The domain of a rational expression is the set of real numbers for which the expression is defined. </li></ul><ul><li>The domain consists of all real numbers except those that make the denominator 0. </li></ul>
4. 4. Domain of a Rational Expression <ul><li>For example, to find the domain of </li></ul><ul><li>solve as follows, </li></ul><ul><li>or </li></ul><ul><li>or </li></ul><ul><li>The domain is </li></ul>
5. 5. Lowest Terms of a Rational Expression Fundamental Principle of Fractions
6. 6. Writing Rational Expressions in Lowest Terms <ul><li>Example Write each rational expression in lowest terms. </li></ul><ul><li>(a) (b) </li></ul><ul><li>Solution </li></ul><ul><li>(a) </li></ul><ul><li>by the fundamental principle, provided p is not 0 or –4. </li></ul>
7. 7. Writing Rational Expressions in Lowest Terms <ul><li>Solution </li></ul><ul><li>(b) </li></ul><ul><li>by the fundamental principle. </li></ul>
8. 8. Multiplying and Dividing Rational Expressions Multiplying and Dividing Fractions For fractions and and
9. 9. Multiplying and Dividing Rational Expressions <ul><li>Example Multiply or divide as indicated. </li></ul><ul><li>(a) (b) </li></ul><ul><li>Solution </li></ul><ul><li>(a) </li></ul>
10. 10. Multiplying and Dividing Rational Expressions <ul><li>Solution (b) </li></ul>
11. 11. Complex Fractions <ul><li>Complex fractions are those fractions whose numerator & denominator both contain fractions. </li></ul>
12. 12. Now you try! <ul><li>Pg 476- 477 </li></ul><ul><li>#’s 14-22 evens </li></ul><ul><li>#’s 26-34 evens </li></ul><ul><li>#’s 36, 37, 38 </li></ul>
13. 13. Adding and Subtracting Rational Expressions Adding and Subtracting Fractions For fractions and and <ul><li>Addition and subtraction are typically performed using the </li></ul><ul><li>least common denominator. </li></ul>
14. 14. Adding and Subtracting Rational Expressions <ul><li>Finding the Least Common Denominator (LCD) </li></ul><ul><li>Write each denominator as a product of prime factors. </li></ul><ul><li>Form a product of all the different prime factors. Each factor should have as exponent the greatest exponent that appears on that factor. </li></ul>
15. 15. Adding/Subtracting <ul><li>when we talk about CDs, we mean denominators that contain the same factors. </li></ul><ul><li>To find our CD, we will first factor the ones we have. </li></ul><ul><li>Then we will multiply each denominator by the factors it is missing to create a CD. </li></ul><ul><li>Remember, we must also multiply the numerator by that same factor. </li></ul>
16. 16. Adding and Subtracting Rational Expressions <ul><li>Example Add or subtract, as indicated. </li></ul><ul><li>(a) (b) </li></ul><ul><li>Solution </li></ul><ul><li>(a) Step 1: Find the LCD </li></ul>
17. 17. Adding and Subtracting Rational Expressions <ul><li>Solution (a) The LCD is </li></ul><ul><li>Then </li></ul>
18. 18. Adding and Subtracting Rational Expressions <ul><li>Solution (b) </li></ul>
19. 19. Now you try! <ul><li>Pg 482- 483 #’s 26-36 evens </li></ul>
20. 20. Complex Fractions <ul><li>A complex fraction is any quotient of two rational expressions. </li></ul>
21. 21. Simplifying Complex Fractions <ul><li>Example Simplify </li></ul><ul><li>Solution </li></ul><ul><li>Multiply both numerator and denominator by the LCD </li></ul><ul><li>of all the fractions a ( a + 1). </li></ul>
22. 22. Simplifying Complex Fractions <ul><li>Solution </li></ul>
23. 23. Now you try! <ul><li>Pg 483 #’s 40 </li></ul>