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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.

## 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.

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. 1 1 1 1 Next…

21. Now you try to simplify the expression:

22. Now try these on your own.