Concept explainers
To find: The partial fraction decomposition of the given rational expression.
Answer to Problem 53E
The partial fraction decomposition of the given rational expression is
Explanation of Solution
Given information:
The rational expression is
Calculations:
The factored form of the denominator
Based on the factors of the denominator, the decomposition form is as follows:
Now, multiply each side by the least common multiple,
That is,
Comparing the coefficients of like terms, we get
Using
Substituting the value in the first equation, we get
Now, adding this equation to the second equation, we get
Using this,
Therefore, the partial fraction decomposition of the given rational expression is
Conclusion:
Using Desmos graphing utility, we can observe that both curves are overlapping each other.
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
- 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