Find the partial fraction decomposition of the rational function.

philosphy111of 2021-11-20 Answered
Find the partial fraction decomposition of the rational function.
\(\displaystyle{\frac{{{x}^{{{3}}}-{2}{x}^{{{2}}}-{4}{x}+{3}}}{{{x}^{{{4}}}}}}\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Alrew1959
Answered 2021-11-21 Author has 836 answers
Step 1
Given: \(\displaystyle{\frac{{{x}^{{{3}}}-{2}{x}^{{{2}}}-{4}{x}+{3}}}{{{x}^{{{4}}}}}}\)
To Find: Partial fraction decomposition
Step 2
Explanation:
As denominator cannot be factored so partial fractions can be calculated.
We can only just divide termwise
\(\displaystyle{\frac{{{x}^{{{3}}}-{2}{x}^{{{2}}}-{4}{x}+{3}}}{{{x}^{{{4}}}}}}={\frac{{{x}^{{{3}}}}}{{{x}^{{{4}}}}}}-{\frac{{{2}{x}^{{{2}}}}}{{{x}^{{{4}}}}}}-{\frac{{{4}{x}}}{{{x}^{{{4}}}}}}+{\frac{{{3}}}{{{x}^{{{4}}}}}}\)
\(\displaystyle={\frac{{{1}}}{{{x}}}}-{\frac{{{2}}}{{{x}^{{{2}}}}}}-{\frac{{{4}}}{{{x}^{{{3}}}}}}+{\frac{{{3}}}{{{x}^{{{4}}}}}}\)
Have a similar question?
Ask An Expert
0
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-11-17
Write the partial fraction decomposition of the given rational expression.
\(\displaystyle{\frac{{{1}}}{{{x}^{{{3}}}-{1}}}}=?\)
What is the partial fraction decomposition?
asked 2021-10-13
Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients.
a) \(\displaystyle{\frac{{{x}^{{4}}+{6}}}{{{x}^{{5}}+{7}{x}^{{3}}}}}\)
b) \(\displaystyle{\frac{{{2}}}{{{\left({x}^{{2}}-{9}\right)}^{{2}}}}}\)
asked 2021-09-26
Find the partial fraction decomposition.
\(\displaystyle{\frac{{{x}^{{{2}}}+{x}-{6}}}{{{\left({x}^{{{2}}}+{1}\right)}{\left({x}-{1}\right)}}}}\)
asked 2021-10-25
Write an informal explanation of partial fraction decomposition.
asked 2021-10-22
Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on.
\(\displaystyle{\frac{{{x}-{14}}}{{{x}^{{2}}-{3}{x}}}}\)
asked 2021-08-15
To find:
The partial fraction decomposition for the rational expression \(\displaystyle{\frac{{{11}-{2}{x}}}{{{x}^{{{2}}}-{8}{x}+{16}}}}\).
asked 2021-10-10
(a) How do we express a rational function r as a partial frac- tion decomposition?
(b) Give the form of the partial fraction decomposition.
\(\displaystyle{\left({i}\right)}{\frac{{{2}{x}}}{{{\left({x}-{5}\right)}{\left({x}-{1}\right)}^{{2}}}}}\)
\(\displaystyle{\left({i}{i}\right)}{\frac{{{2}{x}}}{{{\left({x}-{5}\right)}{\left({x}^{{2}}+{1}\right)}}}}\)
\(\displaystyle{\left({i}{i}{i}\right)}{\frac{{{3}{x}+{1}}}{{{x}{\left({x}^{{2}}+{1}\right)}^{{2}}}}}\)
...