Find the form of the partial fraction decomposition of: 1. x^4+6 P

Bergen 2021-10-31 Answered
Find the form of the partial fraction decomposition of:
1. \(\displaystyle{x}^{{4}}+{6}\)
\(\displaystyle{x}^{{5}}+{7}{x}^{{3}}\)
2. 2 \(\displaystyle{\left({x}^{{2}}-{9}\right)}^{{2}}\)

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Expert Answer

SoosteethicU
Answered 2021-11-01 Author has 8465 answers
1. \(\displaystyle\frac{{{x}^{{4}}+{6}}}{{{x}^{{5}}+{7}{x}^{{3}}}}=\frac{{{x}^{{4}}+{6}}}{{{x}^{{3}}{\left({x}^{{2}}+{7}\right)}}}\)
The partial fraction:
\(\displaystyle=\frac{{A}}{{x}}+\frac{{B}}{{x}^{{2}}}+\frac{{C}}{{x}^{{3}}}+\frac{{{D}{x}+{E}}}{{{x}^{{2}}+{7}}}\)
Where A-E are constants.
2. \(\displaystyle\frac{{2}}{{{\left({x}^{{2}}-{9}\right)}^{{2}}}}=\frac{{2}}{{{\left({\left({x}+{3}\right)}{\left({x}-{3}\right)}\right)}^{{2}}}}\)
\(\displaystyle=\frac{{2}}{{{\left({x}+{3}\right)}^{{2}}{\left({x}-{3}\right)}^{{2}}}}\)
The partial fraction:
\(\displaystyle=\frac{{A}}{{{x}+{3}}}+\frac{{B}}{{{\left({x}+{3}\right)}^{{2}}}}+\frac{{C}}{{{x}-{3}}}+\frac{{D}}{{{\left({x}-{3}\right)}^{{2}}}}\)
Where A-D are constants.
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