Concept explainers
The partial fraction decomposition of the given rational function.
Answer to Problem 1P
Solution:
The partial fraction decomposition of the given rational function is
Explanation of Solution
Given:
The given rational function is,
Approach:
The standard way to find the partial fraction of the rational function,
1. Determine the general form of the partial fraction decomposition of
2. Multiply both the resulting decomposition by
3. Equate the equation in order to determine the constants in the partial fraction decomposition.
Calculation:
Consider the given rational function,
Write the general form of the partial fraction decomposition of the above given rational function.
Multiply both sides of this equation by
Equate the coefficient of like powers of
Consequently,
Substitute the values of
Therefore, the partial fraction decomposition of the given rational function is
Conclusion:
Hence, the partial fraction decomposition of the given rational function is
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Chapter B Solutions
Differential Equations and Linear Algebra (4th Edition)
- Match the rational expression on the left with the correct partial fraction decomposition form on the right. 62. x2-2x+3x2x-4x3+5 a. Ax+Bx2+Cx3+Dx4+Ex-4+Fx+Gx2+5 b. Ax+Bx-4+Cx-42+Dx-43+Fx+Gx2+5+Hx+Ix2+52 c. Ax+Bx2+Cx-4+Dx2+Ex+Fx3+5 d. Ax+Bx2+Cx3+Dx-4+Ex-42+Fx+Gx2+5 e. Ax+Bx-4+Cx+Dx2+5 f. Ax+Bx2+Cx-4+Dx+Ex2+5arrow_forwardDecompose into partial fractions. 4x3+3x+x2+2x4+x2arrow_forward
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