Question

Find the form of the partial fraction decomposition of:1.x^4+6 , x^5+7x^3 2. 2 (x^2-9)^2

Trigonometric functions
ANSWERED
asked 2021-09-14

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

Expert Answers (1)

2021-09-15
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.
2
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...