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UNIT: RATIONAL FUNCTIONS 9-4: RATIONAL EXPRESSIONS DAY 1 (SIMPLIFICATION) Essential Question: How do you simplify, multiply and divide rational expressions?

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9-4: Rational Expressions A rational expression is in simplest form when its numerator and denominator are polynomials which have no common divisors. Examples in simplest form: Not in simplest form:

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9-4: Rational Expressions To simplify a rational expression: Remove any GCFs that may exist Factor if possible Cancel common factors (parenthesis must match) To find restrictions: Before canceling out anything, check the denominators Set any denominator pieces equal to 0 These give you numbers your variable cannot be

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9-4: Rational Expressions Example Simplify. State any restrictions on the variables. Factor x 2 + 10x + 25 Factor x 2 + 9x + 20 Restrictions: (x + 5)(x + 5) (x + 4)(x + 5) x ≠ -4, x ≠ -5

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9-4: Rational Expressions Your Turn #1 (Already simplified, just reduce) Simplify. State any restrictions on the variables. Restrictions: Simplified: x ≠ 0, y ≠ 0

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9-4: Rational Expressions Your Turn #2 (GCF & Factor) Simplify. State any restrictions on the variables. Simplify -6 – 3x Factor x 2 – 6x + 8 Restrictions: x ≠ 2, x ≠ 4 -3(x + 2) (x – 2)(x – 4)

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9-4: Rational Expressions Your Turn #3 (Factor top & bottom) Simplify. State any restrictions on the variables. Factor 2x 2 – 3x – 2 Factor x 2 – 5x + 6 Restrictions: (2x + 1)(x – 2) (x – 2)(x – 3) x ≠ 2, x ≠ 3

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9-4: Rational Expressions Assignment Page 511 Problems 1 – 6, all You must show your work

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UNIT: RATIONAL FUNCTIONS 9-4: RATIONAL EXPRESSIONS DAY 2 (MULTIPLICATION) Essential Question: How do you simplify, multiply and divide rational expressions?

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9-4: Rational Expressions To multiply rational expressions: Remove any GCFs that may exist Factor if possible Cancel common factors (parenthesis must match) Multiply numerators with numerators, denominators with denominators To find restrictions: Before canceling out anything, check all denominators Set any denominator pieces equal to 0 These give you numbers your variable cannot be

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9-4: Rational Expressions Example Multiply and. State any restrictions on the variables. Factor 2x 2 + 7x + 3 Factor x 2 – 16 Factor x 2 + 8x + 15 Simplified: Restrictions: (2x + 1)(x + 3) (x – 4)(x + 4) x ≠ 4, x ≠ -5, x ≠ -3 (x + 5)(x + 3)

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9-4: Rational Expressions Y OUR T URN Multiply and. State any restrictions on the variables. Factor x 2 – 4 Factor x 2 – 1 Factor x 2 + 2x Simplified: Restrictions: (x + 2)(x – 2) (x + 1)(x – 1) x ≠ -1, x ≠ 1, x ≠ 0, x ≠ -2 x(x + 2)

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UNIT: RATIONAL FUNCTIONS 9-4: RATIONAL EXPRESSIONS DAY 3 (DIVISION) Essential Question: How do you simplify, multiply and divide rational expressions?

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9-4: Rational Expressions To divide rational expressions: Remove any GCFs that may exist Factor if possible Flip division sign to multiplication, flip fraction after division sign Cancel common factors (parenthesis must match) Multiply numerators with numerators, denominators with denominators To find restrictions: Before canceling out anything, check all denominators Set any denominator pieces equal to 0 These give you numbers your variable cannot be Restrictions must be checked both before and after the flip

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9-4: Rational Expressions Example Divide by. State any restrictions on the variables. Fix 4 – x (always want x to come first and be positive) Flip division into multiplication Simplified: Restrictions: -1(x – 4) x ≠ - 2 / 3, x ≠ 2, y ≠ 5 / 7, x ≠ 4

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9-4: Rational Expressions Y OUR T URN Divide by. State any restrictions on the variables. Factor x 2 +2x – 15 Factor x 2 – 16 Factor 3x – 12 Flip division into multiplication: Restrictions:Simplified: (x + 5)(x – 3) (x + 4)(x – 4) 3(x – 4) x ≠ 4, x ≠ -4, x ≠ -1

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9-4: Rational Expressions Assignment Page 511 Problems 7 – 18, all You must show your work

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