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USPshnik [31]
3 years ago
13

Can parts of a system also be a system?

Biology
1 answer:
jonny [76]3 years ago
7 0

Answer:

yes A system can be also be a system

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Write out the form of the partial fraction decomposition of the function (See Example). Do not determine the numerical values of
maw [93]

Answer:

a.\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{Dx+E}{x^2+5}

b.\frac{A}{x+3}+\frac{B}{x-3}+\frac{C}{(x-3)^2}+\frac{D}{(x+3)^2}

Explanation:

a.We are given that

\frac{x^4+7}{x^5+5x^3}

\frac{x^4+7}{x^5+5x^3}=\frac{x^4+7}{x^3(x^2+5)}

Using partial fraction decomposition of the given function

\frac{x^4+7}{x^3(x^2+5)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{Dx+E}{x^2+5}

Using the formula

\frac{1}{x^3(x^2+a)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{Dx+E}{x^2+a}

b.\frac{2}{(x^2-9)^2}

\frac{2}{(x^2-3^2)^2}=\frac{2}{(x+3)^2(x-3)^2}

Using property a^2-b^2=(a+b)(a-b)

\frac{2}{(x+3)^2(x-3)^2}=\frac{A}{x+3}+\frac{B}{x-3}+\frac{C}{(x-3)^2}+\frac{D}{(x+3)^2}

Using the property

\frac{1}{x^2}=\frac{A}{x}+\frac{B}{x^2}

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