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Warm Up Simplify each expression. Assume all variables are nonzero.

Learn how to simplify, multiply, and divide rational expressions with step-by-step examples. Practice and improve your skills in simplifying and performing operations on rational expressions.

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Warm Up Simplify each expression. Assume all variables are nonzero.

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  1. 1 y2 x6 y5 y3 x2 Warm Up Simplify each expression. Assume all variables are nonzero. 1.x5x2 x7 2.y3y3 y6 3. 4. x4 Factor each expression. 5. x2 – 2x – 8 (x – 4)(x + 2) 6. x2 – 5x x(x – 5) 7. x5 – 9x3 x3(x – 3)(x + 3)

  2. 4B.1 Simplifying, Multiplying, and Dividing Rational Expressions Holt McDougal Algebra 2 Holt Algebra 2

  3. Objectives Simplify rational expressions. Multiply and divide rational expressions.

  4. Vocabulary rational expression

  5. A rational expression is a quotient of two polynomials. Other examples of rational expressions include the following:

  6. Steps to simplify: • Factor numerator & denominator • State excluded values • Set each factor in the denominator equal to zero and solve. • Only for simplifying • Simplify by cancelling out like factors on top and bottom.

  7. SIMPLIFYING

  8. 510x8 – 4 36 10x8 6x4 Example 1A: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined.

  9. (x+ 2)(x – 1) x2 + x – 2 (x+ 2) (x – 1)(x + 3) x2 + 2x – 3 (x + 3) Example 1B: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. Factor; then divide out common factors. =

  10. 28x11 – 2 18 (3x + 4) 3x + 4 16x11 1 (3x + 4)(x – 1) 3x2 + x – 4 (x – 1) 8x2 You Try!Simplify. Identify any x-values for which the expression is undefined. Example 1C Example 1D

  11. MULTIPLYING

  12.   10x3y4 3x5y3 x – 3 x – 3 x + 5 x + 5 (x – 3)(x + 3) 4x+ 20 4(x+ 5) x2 – 9 9x2y5 2x3y7 Multiply. Assume all expressions are defined. 2A. 2B.

  13. x x7    15 2x 10x – 40 x + 3 20 x2 – 6x + 8 5x + 15 x4 You Try!Multiply. Assume that all expressions are defined. Example 2C Example 2D

  14. DIVIDING • Keep • Change • Flip • (then the problem becomes multiplication)

  15. 15 8y5 5x4 5x4 8y5 15 ÷  8x2y2 8x2y2 Example 3A: Dividing Rational Expressions Divide. Assume that all expressions are defined.

  16. ÷   (x + 3)(x – 4) x4+ 2x3 – 8x2 x2(x2 – 9) x4– 9x2 x4– 9x2 x2 – 16 x2 – 16 (x – 1)(x – 2) x2(x2 + 2x – 8) x4+ 2x3 – 8x2 x2 – 4x + 3 x2 – 4x + 3 x2 – 4x + 3 x2 – 16 Example 3B: Dividing Rational Expressions Divide. Assume that all expressions are defined.

  17. ÷ x2 x4y ÷ 4 12y2 2x2– 7x – 4 4x2– 1 8x2 – 28x +12 x2 – 9 You Try!Divide. Assume that all expressions are defined. Example 3C Example 3D

  18. Ready to Practice?

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