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Simplify, Multiply and Divide Rational Expressions

Simplify, Multiply and Divide Rational Expressions. Section 8-2. Simplify. Example 1. Simplify. Example 2. 2. 1. Example 3. Simplify. ( x + 3) ( x + 3). ( x + 3) ( x - 3). Example 4. Simplify. Rules of Multiplying Expressions.

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Simplify, Multiply and Divide Rational Expressions

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  1. Simplify,Multiply and Divide RationalExpressions Section 8-2 10.3 Multiplying and Dividing Expressions

  2. Simplify Example 1

  3. Simplify Example 2 2 1

  4. Example 3 Simplify (x + 3) (x + 3) (x + 3) (x - 3) 10.3 Multiplying and Dividing Expressions

  5. Example 4 Simplify 10.3 Multiplying and Dividing Expressions

  6. Rules of Multiplying Expressions Take GCF of numerator(s) and denominator(s) if possible. Factor the numerator(s) and denominator (s) Cancel [up and down OR diagonally] out the factors if needed, multiply and simplify. 10.3 Multiplying and Dividing Expressions

  7. Example 5 Simplify 2 2 10.3 Multiplying and Dividing Expressions

  8. Example 6 Simplify 10.3 Multiplying and Dividing Expressions

  9. Undefined Values Any number substituted into a variable which makes the expression in the denominatorequal to zero, it will cause the equation to be undefined. Quick Steps: After factoring an expression, put all factors equal to zero Solve for the variable Answers are the restrictions 10.3 Multiplying and Dividing Expressions

  10. Example 7 Simplify . Identify any x-values for which the expression is undefined. (3x + 4) (3x + 4)(x – 1) 10.3 Multiplying and Dividing Expressions

  11. Example 8 Simplify Identify any x-values for which the expression is undefined. (2x + 1) (2x – 3) 10.3 Multiplying and Dividing Expressions

  12. Example 9 Simplify . Identify any x-values for which the expression is undefined. –1(x)(x – 4) –x –1(x2 – 4x) (x – 4)(x + 2) (x + 2 ) x2 – 2x – 8 Factor out –1 in the numerator so that x2 is positive, and reorder the terms. Factor the numerator and denominator. Divide out common factors. Simplify. 10.3 Multiplying and Dividing Expressions

  13. Rules of Divide Expressions Take GCF of numerator(s) and denominator(s) if possible. Take the reciprocal (flip) of the second fraction. Factor the numerator(s) and denominators into simplest form Cancel out the factors and cancel if needed, Multiply and simplify 10.3 Multiplying and Dividing Expressions

  14. Example 10 2 2 10.3 Multiplying and Dividing Expressions

  15. Example 11 Simplify 10.3 Multiplying and Dividing Expressions

  16. Example 12 Simplify 10.3 Multiplying and Dividing Expressions

  17. Your Turn Simplify and/or solve these problems 1. 2. 3. 4. 5. 4x2 – 9 = 5 2x +3 6x – x2 x2 – 7x + 6 10.3 Multiplying and Dividing Expressions

  18. Example 13 Simplify 10.3 Multiplying and Dividing Expressions

  19. Example 14 Solve. Check your solution and list restrictions of = 14 (x+ 5)(x – 5) (x – 5) Note that x ≠ 5. x + 5 = 14 x = 9 10.3 Multiplying and Dividing Expressions

  20. Example 15 Solve. Check your solution and list restrictions of 10.3 Multiplying and Dividing Expressions

  21. Assignment Pg 580: 18 - 31 10.3 Multiplying and Dividing Expressions

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