actever6a

2021-11-16

To calculate: The pardital decomposition of the function $\frac{-12x-29}{2{x}^{2}+11x+15}$

Fommeirj

Beginner2021-11-17Added 11 answers

Given Information:

The provided expression is:

Formula used:

Decomposition of

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.

Calculation:

Consider the provided expression,

Here,

Factorize g(x):

So, the expression can be written as:

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