Concept explainers
To express: The expression
Answer to Problem 11AYU
The expression
Explanation of Solution
Given information:
The expression
Formula used:
Improper rational expression of the form
Calculation:
Consider the expression
Observe that the degree of the numerator of the rational expression is greater than or equal to the denominator so the provided expression is improper.
When a polynomial is divided by its factor then dividend is the product of divisor and quotient increased by remainder.
Apply the method of long division.
Now, since
Therefore,
Recall that improper rational expression of the form
Rewrite the expression
Therefore,
Now, solve the above expression for values of A and B .
Now, equate the coefficients on both the side of equation to obtain
Now, solve the two equations involving two variables.
From equation
Now substitute
Now substitute
Now, substitute the values of A and B in the partial fraction decomposition.
Therefore,
Thus, the expression
Chapter 11 Solutions
Precalculus
Additional Math Textbook Solutions
Calculus: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (3rd Edition)
Glencoe Math Accelerated, Student Edition
Calculus and Its Applications (11th Edition)
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