To calculate: The pardital decomposition of the function \frac{-12x



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To calculate: The pardital decomposition of the function 12x292x2+11x+15

Answer & Explanation



Beginner2021-11-17Added 11 answers

Given Information:
The provided expression is:12x292x2+11x+15.
Formula used:
Decomposition of f(x)g(x) into Partial Fractions:
Consider a rational expression f(x)g(x), where f(x) and g(x) are polynomial with real coefficients, g(x)0, and the degree of f(x) is less than degree of g(x).
Step 1: Factor the denominator g (x) completely into linear factors of the form (ax+b)m and quadratic factors of the form (ax2+bx+c)n that are not further factorable over the integers.
Step 2: Set up the form of decomposition. That is, write the original rational expression f(x)g(x) as a sum of simpler fractions using these guidelines. Note that A1,A2,..,Am,B1,B2,..,BmandC1,C2,.,Cm are constants.
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,
Here, f(x)=12x29andg(x)=2x2+11x+15
Factorize g(x):
So, the expression can be written as:

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