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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 can not = 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 can not = 0. Now,lets go through the steps to simplify a rational expression.

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

  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 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. Remember how to multiply fractions: First you multiply the numerators then multiply the denominators.

  14. 1 1 1 1 1 1 1 1 1 The same method can be used to multiply rational expressions.

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

  16. 1 1 1 1 1 1 Step #2: Divide the numerator and denominator by the common factors.

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

  18. 1 5 1 4 Multiply by the reciprocal of the divisor.

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

  20. 1 1 1 1 Next

  21. Now you try to simplify the expression:

  22. Now try these on your own.

  23. Here are the answers:

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