# Find the partial fraction decomposition of the rational function.

Find the partial fraction decomposition of the rational function.
$$\displaystyle{\frac{{{x}^{{{3}}}-{2}{x}^{{{2}}}-{4}{x}+{3}}}{{{x}^{{{4}}}}}}$$

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Alrew1959
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
$$\displaystyle{\frac{{{x}^{{{3}}}-{2}{x}^{{{2}}}-{4}{x}+{3}}}{{{x}^{{{4}}}}}}={\frac{{{x}^{{{3}}}}}{{{x}^{{{4}}}}}}-{\frac{{{2}{x}^{{{2}}}}}{{{x}^{{{4}}}}}}-{\frac{{{4}{x}}}{{{x}^{{{4}}}}}}+{\frac{{{3}}}{{{x}^{{{4}}}}}}$$
$$\displaystyle={\frac{{{1}}}{{{x}}}}-{\frac{{{2}}}{{{x}^{{{2}}}}}}-{\frac{{{4}}}{{{x}^{{{3}}}}}}+{\frac{{{3}}}{{{x}^{{{4}}}}}}$$