Concept explainers
To find:The partial fraction decomposition of the given proper rational expression.
Answer to Problem 36E
The partial fraction decomposition of the given rational expression is
Explanation of Solution
Given information:
The proper rational expression is
Calculations:
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
Assing 2 times the first equation with the second equation to produce a new second equation and subtracting 3 times the first equation from the third equation to produce a new third equation, we get
Adding second and third equations to produce a new third equation results
Now, solving
Substituting this value in the second equation, we get
Substituting these values in the first equation, we get
Conclusion:
Therefore, the partial fraction decomposition of the given rational expression is
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