Write out the form of the partial fraction decomposition of the function x4 – 2x3 + x2 + 7x – 6 (a) x2 - 2x + 1 x2 - 1 (b) x3 + x2 + x

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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This is discrete mathematics

**Partial Fraction Decomposition Example**

The task is to write out the form of the partial fraction decomposition of the given functions, as demonstrated in an example linked previously.

---

**Problem (a):**

Function:
\[
\frac{x^4 - 2x^3 + x^2 + 7x - 6}{x^2 - 2x + 1}
\]

- There is an empty box provided for writing the decomposition.
- A red "X" beside the box indicates that the current decomposition attempt is incorrect.

---

**Problem (b):**

Function:
\[
\frac{x^2 - 1}{x^3 + x^2 + x}
\]

- Another empty box is provided for entering the decomposition.
- Similarly, a red "X" beside this box suggests the attempt is incorrect.

---

In both parts, the task involves breaking down the given rational functions into simpler fractions that can be more easily integrated or manipulated.
Transcribed Image Text:**Partial Fraction Decomposition Example** The task is to write out the form of the partial fraction decomposition of the given functions, as demonstrated in an example linked previously. --- **Problem (a):** Function: \[ \frac{x^4 - 2x^3 + x^2 + 7x - 6}{x^2 - 2x + 1} \] - There is an empty box provided for writing the decomposition. - A red "X" beside the box indicates that the current decomposition attempt is incorrect. --- **Problem (b):** Function: \[ \frac{x^2 - 1}{x^3 + x^2 + x} \] - Another empty box is provided for entering the decomposition. - Similarly, a red "X" beside this box suggests the attempt is incorrect. --- In both parts, the task involves breaking down the given rational functions into simpler fractions that can be more easily integrated or manipulated.
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