Concept explainers
To write: the form of the partial function decomposition of the rational expression and check result algebraically by combining fractions and check result graphically by using a graphing utility to graph the rational expression and the partial fraction in the same viewing window.
Answer to Problem 66E
Explanation of Solution
Given information: Given rational function is
Calculation:
Given function is,
Since the degree of the numerator is not less than degree of the denominator perform polynomial long division.
Now, deal with
The form of the partial fraction decomposition is,
Since both sides are in standard form, can equate the coefficients to come up with a system of equations.
Recombine to check algebraically.
Graph of the original function and the partial fraction decomposition is given below.
Graph of the original function and the partial fraction decomposition. They’re both there and overlap because they’re equal.
Chapter 7 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning