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Simplifying

Simplifying. Rational Expressions. Multiplying and Dividing Rational Expressions. Remember that a rational number can be expressed as a quotient of two integers . A rational expression can be expressed as a quotient of two polynomials. Remember, denominators cannot = 0.

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Simplifying

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  1. Simplifying Rational Expressions

  2. Multiplying and Dividing Rational Expressions Remember that a rational number can be expressed as a quotient of two integers. A rational expression can be expressed as a quotient of two polynomials.

  3. Remember, denominators cannot = 0. Now, let’s go through the steps to simplifya rational expression.

  4. Step 1: Factor the numerator and the denominator completely looking for common factors: Numerator: Denominator:

  5. What is the common factor? Step 2: Divide the numerator and denominator by the common factor.

  6. 1 1 Step 3: Multiply to get your answer.

  7. Looking at the answer from the previous example … what value of x would make the denominator 0? x = (-1) makes the denom=0 The expression is undefined when the values make the denominator equal to 0

  8. How do I find the values that make an expression undefined? Completely factor the original denominator.

  9. Factor the denominator The expression is undefined when: a= 0, 2, and -2 and b= 0.

  10. Lets go through another example. Factor out the GCF Next

  11. 1 1

  12. Now try to do some on your own. Also find the values that make each expression undefined??

  13. 5x³ + 10x² = 5x²(x + 2) • x³ - 6x² - 16x x(x² - 6x – 16) • = 5x²(x + 2) • x(x – 8)(x + 2) • Cancel out both (x + 2)’s • = 5x² = 5x • x(x – 8) (x – 8) • x² - 5x + 6 = (x – 2)(x – 3) • x² - 9 (x + 3)(x – 3) • Cancel out both (x – 3)’s • = (x – 2) • (x + 3)

  14. Do you remember how to multiply fractions?? First you multiply the numerators then multiply the denominators.

  15. 1 1 1 1 1 1 1 1 1 The same method can be used to multiply rational expressions.

  16. Let’s do another one. Step #1: Factor the numerator and the denominator. Next

  17. 1 1 1 1 1 1 Step #2: Divide the numerator and denominator by the common factors.

  18. Step #3: Multiply the numerator and the denominator. Remember how to divide fractions?

  19. 1 5 1 4 Multiply by the reciprocal of the divisor.

  20. Dividing rational expressions uses the same procedure. Ex: Simplify

  21. 1 1 1 1 Next…

  22. Now you try to simplify the expression:

  23. Now try these on your own.

  24. Here are the answers:

  25. Now wasn’t that fun???!!! Your homework is:

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