1 / 17

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.

amy
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related