Simplify each expression. Assume all variables are nonzero. Warm Up Simplify each expression. Assume all variables are nonzero. 1. x5  x2 x7 2. y3  y3 y6 3. x6 x2 4. y2 y5 1 y3 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)

This weeks required assignments for today no extension: Algebra 1- AA1, AA2 IXL Proficiency -85% Algebra 2- N4 TODAY- Friday 3/22 Algebra 1- Y3, Y5, V8 - 90% proficiency Extra Credit (must have completed all of the above for Extra Credit PRIOR TO COMPLETING) 8th Grade math ( BB6, BB7) – 95% proficiency

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

Objectives Simplify rational expressions. Multiply and divide rational expressions.

Vocabulary rational expression

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

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.

SIMPLIFYING

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

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

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

MULTIPLYING

Sponge 3-25-19 Simplify each. Then solve the denominators to find what is know as the “excluded values” (this means x cannot be this value so we exclude it). 16x11 8x2 3x + 4 3x2 + x – 4 1. 2.

Multiply. Assume all expressions are defined. 3x5y3 2x3y7  10x3y4 9x2y5 x – 3 4x + 20  x + 5 x2 – 9 1A. 1B. x – 3 4(x + 5)  x + 5 (x – 3)(x + 3)

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

(then the problem becomes multiplication) DIVIDING STEPS Keep Change Flip (then the problem becomes multiplication)

Example 1A: Dividing Rational Expressions Divide. Assume that all expressions are defined. 5x4 8x2y2 ÷ 8y5 15 5x4 8x2y2  15 8y5

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

2A You Try! Divide. Example 3C Example 3D x2 4 ÷ 12y2 x4y 2x2 – 7x – 4 x2 – 9 ÷ 4x2– 1 8x2 – 28x +12

Copy each and complete. I know…. There is not a #1, nor 5-7).

Back of handout from last week with checks! HW

Week of 3-18 This weeks required IXL assignments After Classwork! Part 1 must be completed “by the end of class” (no late work accepted). Part 1: Algebra 1- AA1, AA2, GG3 IXL Proficiency -85% Algebra 2- N4 Now “TODAY”- Friday 3/22 Algebra 1- Y3, Y5, V8 - 90% proficiency Extra Credit (must have completed all of the above for Extra Credit PRIOR TO COMPLETING) 8th Grade math ( BB6, BB7) – 95% proficiency