Key to "Find the form of the partial fraction decomposition..."

Bergen

Answered question

2021-10-31

Find the form of the partial fraction decomposition of:
1.

x^{4} + 6

x^{5} + 7 x^{3}

2. 2

{(x^{2} - 9)}^{2}

SoosteethicU

Skilled2021-11-01Added 102 answers

\frac{x^{4} + 6}{x^{5} + 7 x^{3}} = \frac{x^{4} + 6}{x^{3} (x^{2} + 7)}

The partial fraction:

= \frac{A}{x} + \frac{B}{x^{2}} + \frac{C}{x^{3}} + \frac{D x + E}{x^{2} + 7}

Where A-E are constants.
2.

\frac{2}{{(x^{2} - 9)}^{2}} = \frac{2}{{((x + 3) (x - 3))}^{2}}

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

The partial fraction:

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

Where A-D are constants.

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