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Unit: Rational Functions 9-4: Rational Expressions Day 1 (Simplification)

Unit: Rational Functions 9-4: Rational Expressions Day 1 (Simplification). Essential Question: How do you simplify, multiply and divide rational expressions?. 9-4: Rational Expressions.

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Unit: Rational Functions 9-4: Rational Expressions Day 1 (Simplification)

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  1. Unit: Rational Functions9-4: Rational ExpressionsDay 1 (Simplification) Essential Question: How do you simplify, multiply and divide rational expressions?

  2. 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:

  3. 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

  4. 9-4: Rational Expressions • Example • Simplify . State any restrictions on the variables. • Factor x2 + 10x + 25 • Factor x2 + 9x + 20 • Restrictions: (x + 5)(x + 5) (x + 4)(x + 5) x ≠ -4, x ≠ -5

  5. 9-4: Rational Expressions • Your Turn #1 (Already simplified, just reduce) • Simplify . State any restrictions on the variables. • Restrictions: • Simplified: x ≠ 0, y ≠ 0

  6. 9-4: Rational Expressions • Your Turn #2 (GCF & Factor) • Simplify . State any restrictions on the variables. • Simplify -6 – 3x • Factor x2 – 6x + 8 • Restrictions: -3(x + 2) (x – 2)(x – 4) x ≠ 2, x ≠ 4

  7. 9-4: Rational Expressions • Your Turn #3 (Factor top & bottom) • Simplify . State any restrictions on the variables. • Factor 2x2 – 3x – 2 • Factor x2 – 5x + 6 • Restrictions: (2x + 1)(x – 2) (x – 2)(x – 3) x ≠ 2, x ≠ 3

  8. 9-4: Rational Expressions • Assignment • Page 511 • Problems 1 – 6, all • You must show your work

  9. Unit: Rational Functions9-4: Rational ExpressionsDay 2 (Multiplication) Essential Question: How do you simplify, multiply and divide rational expressions?

  10. 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

  11. 9-4: Rational Expressions • Example • Multiply and . State any restrictions on the variables. • Factor 2x2 + 7x + 3 • Factor x2 – 16 • Factor x2 + 8x + 15 • Simplified: • Restrictions: (2x + 1)(x + 3) (x – 4)(x + 4) (x + 5)(x + 3) x ≠ 4, x ≠ -5, x ≠ -3

  12. 9-4: Rational Expressions • Your Turn • Multiply and . State any restrictions on the variables. • Factor x2 – 4 • Factor x2 – 1 • Factor x2 + 2x • Simplified: • Restrictions: (x + 2)(x – 2) (x + 1)(x – 1) x(x + 2) x ≠ -1, x ≠ 1, x ≠ 0, x ≠ -2

  13. Unit: Rational Functions9-4: Rational ExpressionsDay 3 (Division) Essential Question: How do you simplify, multiply and divide rational expressions?

  14. 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 afterthe flip

  15. 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

  16. 9-4: Rational Expressions • Your Turn • Divide by . State any restrictions on the variables. • Factor x2 +2x – 15 • Factor x2 – 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

  17. 9-4: Rational Expressions • Assignment • Page 511 • Problems 7 – 18, all • You must show your work

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