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Adding and Subtracting Rationals

Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

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Page 1: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Adding and Subtracting Rationals

Page 2: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

REVIEW

Page 3: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Review

Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero.

Page 4: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Review

Inverse Variation Function - Graph

Page 5: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Review

Rational Functions - Asymptotes

Page 6: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Review

Rational Functions - Asymptotes

Page 7: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Review

Rational Functions – Sketching the graph

Draw all the asymptotesDetermine where it is positive and

negativeDetermine where it is ZeroSketch

Page 8: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Review

Rational Expressions – Multiplication / Division

Restrictions – When the denominator is zero

When dividing by zero

Simplify by canceling like terms (factors)

Page 9: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

NEW MATERIAL

Page 10: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Addition Subtraction Rationals

Page 11: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Addition Subtraction Rationals

Page 12: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Addition Subtraction Rationals

Page 13: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Addition Subtraction Rationals

Page 14: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Addition Subtraction Rationals

Page 15: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Addition Subtraction Rationals

Page 16: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Addition Subtraction Rationals

Page 17: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Addition Subtraction Rationals

Page 18: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Addition Subtraction Rationals

Page 19: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Addition Subtraction Rationals

Complex Fractions – A fraction that has a fraction in the numerator or denominator

Page 20: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Addition Subtraction Rationals

Page 21: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Addition Subtraction Rationals

Page 22: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Addition Subtraction Rationals

Page 23: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Solving Rational Equations

Page 24: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Solving Rational Equations

Multiplying variables on both sides of an equal sign may introduce extraneous solutions.

Check for extraneous solutions by plugging into the original equation.

Page 25: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Solving Rational Equations

Page 26: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Solving Rational Equations

Page 27: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Solving Rational Equations - Practice

Page 28: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Solving Rational Equations

If rational functions are added in an equation, use the LCD to multiply all terms and “clear” the fraction

Page 29: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Solving Rational Equations – Example

Page 30: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Solving Rational Equations – Example

Page 31: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Solving Rational Equations - Practice

Page 32: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Solving Rational Equations – Example

Page 33: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Solving Rational Equations - Practice

Page 34: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Homework

9-5 Adding and Subtracting RationalsFirst Column

9-6 Solving Rational Expressions

First ColumnEnd at #38

Page 35: Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero

Homework

9-5 Adding and Subtracting RationalsFirst Column


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