Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
Solution
-
Multiply both sides by the common denominator
: -
Expand the right side:
-
Combine like terms on the right:
-
Equate the coefficients of corresponding terms:
- Coefficient of
: - Constant term:
- Coefficient of
-
Solve the system of equations:
From, express as: Substitute into: Simplify: -
Substitute
into : -
The partial fractions decomposition is:
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Extra Insights
To solve the partial fraction, we begin by expressing the equation as follows:
Next, we need to combine the right side over a common denominator:
This gives us:
Now, we can expand the right-hand side:
Next, we group the terms:
Now, we compare the coefficients from both sides. For the coefficients of
And for the constants:
Now we solve these two equations. From equation (1), we can express
Substituting this into equation (2):
Simplifying gives:
Now substituting
Thus, we find:
So, the partial fraction decomposition is:
