Q. 41 Write the partial fraction decom... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 41 (page 765)

Write the partial fraction decomposition of each rational expression.
$\frac{x^{3}}{{(x 2 + 16)}^{3}}$

Short Answer

Expert verified

The partial fraction decomposition is $\frac{x^{3}}{{(x 2 + 16)}^{3}} = \frac{x}{{(x^{2} + 16)}^{2}} + \frac{鈭� 16 x}{{(x^{2} + 16)}^{3}}$

Step by step solution

Step 1. Given Information.

The rational expression is,

$\frac{x^{3}}{{(x^{2} + 16)}^{3}} = \frac{A x + B}{x^{2} + 16} + \frac{C x + D}{{(x^{2} + 16)}^{2}} + \frac{E x + F}{{(x^{2} + 16)}^{3}}$

$\frac{x^{3}}{{(x^{2} + 16)}^{3}} = \frac{{(x^{2} + 16)}^{2}}{(A x + B)} + \frac{(x^{2} + 16)}{(C x + D)} + \frac{E x + F}{{(x^{2} + 16)}^{3}}$

Therefore,

$x^{3} = {(x^{2} + 16)}^{2} (A x + B) + (x^{2} + 16) (C x + D) + E x + F$

$x^{3} = x^{5} A + x^{4} B + 32 x^{3} A + x^{3} C + 32 x^{2} B + x^{2} D + 256 x A + 16 x C + x E + 256 B + 16 D + F$

Therefore,

$A = 0 B = 0 32 A + C = 132 B + D = 0 256 A + 16 C + E = 0 256 B + 16 D + F = 0$

Step 2. Partial Fraction Decomposition.

Decompose the rational fraction, we get,

$A = 0, B = 0, C = 1, D = 0, E = 鈭� 16, F = 0$

Therefore,

role="math" localid="1647535930996" $\frac{x^{3}}{{(x 2 + 16)}^{3}} = \frac{x}{{(x^{2} + 16)}^{2}} + \frac{鈭� 16 x}{{(x^{2} + 16)}^{3}}$

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91影视

Write the partial fraction decomposition of each rational expression.
$\frac{x^{3}}{{(x 2 + 16)}^{3}}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Partial Fraction Decomposition.

One App. One Place for Learning.

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91影视

Write the partial fraction decomposition of each rational expression.x3(x2+16)3

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Partial Fraction Decomposition.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Discrete Mathematics

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Write the partial fraction decomposition of each rational expression.
$\frac{x^{3}}{{(x 2 + 16)}^{3}}$