Beginner2021-11-17Added 11 answers
The provided expression is:
Consider a rational expression
Step 1: Factor the denominator g (x) completely into linear factors of the form
Step 2: Set up the form of decomposition. That is, write the original rational expression
Linear Factors of g(x):
For each linear factor of g(x), the partial fraction decomposition must include the sum:
Quadratic Factors of g (x):
For each quadratic factor of g (x), the partial fraction decomposition must include the sum:
Step 3: With the form of the partial fraction decomposition set up, multiply both sides of the equation by the Least Common Divisor to clear fractions.
Step 4: Use the equation from step3, set up a system of linear equations by equating the constant terms and equating the coefficients of like powers ofx.
Step 5: Solve the system of equations from step4 and substitute the solutions to the system into the partial fraction decomposition.
Consider the provided expression,
So, the expression can be written as:
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