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Question

Match each rational expression with the form of its decomposition. The decompositions are labeled a-h.

$\dfrac{2 x-1}{x^4-16}$

a. $\dfrac{A}{x}+\dfrac{B}{x^2}+\dfrac{C}{x^3}+\dfrac{D}{x-2}+\dfrac{E}{(x-2)^2}$

b. $\dfrac{A}{x}+\dfrac{B}{x^2}+\dfrac{C}{x+2}+\dfrac{D}{x-2}$

c. $\dfrac{A}{x}+\dfrac{B}{x^2}+\dfrac{C}{x^3}+\dfrac{D}{x-2}$

d. $\dfrac{A}{(x+2)}+\dfrac{B}{(x+2)^2}+\dfrac{C}{(x+2)^3}+\dfrac{D}{x-2}$

e. $\dfrac{A x+B}{x^2+4}+\dfrac{C}{x+2}+\dfrac{D}{x-2}$

f. $\dfrac{A}{x}+\dfrac{B}{x^2}+\dfrac{C}{x+2}+\dfrac{D x+E}{x^2+4}$

g. $\dfrac{A}{x+2}+\dfrac{B}{(x+2)^2}+\dfrac{C}{(x+2)^3}+\dfrac{D}{x}+\dfrac{E}{x^2}$

h. $\dfrac{A}{x}+\dfrac{B}{x-2}+\dfrac{C}{(x-2)^2}$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 3Given function:

$\begin{equation*} \dfrac{2x-1}{x^4-16} \end{equation*}$

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