Chapter 11: Q. 13 (page 765)

Write the partial fraction decomposition of each rational expression:
$\frac{4}{x (x - 1)}$ .

Short Answer

Expert verified

The partial fraction decomposition is,

$\frac{4}{x (x - 1)} = \frac{- 4}{x} + \frac{4}{x - 1}$ .

Step by step solution

Step 1. Given Information.

The rational expression is,

$\frac{4}{x (x - 1)}$ .

Step 2. Partial Decomposition.

Decompose the rational expression,

$\frac{4}{x (x - 1)} = \frac{A}{x} + \frac{B}{(x - 1)} . . . . . . . . . . . (1)$

Multiplying each side by $x (x - 1)$ ,

role="math" localid="1647369079514" $4 = A (x - 1) + B x 4 = (A + B) x - A . . . . . . . . . . (2)$

Equating the coefficients of like powers, we get,

$A + B = 0 - A = 4$

Solving the two equations,

$A = - 4 B = 4$

The partial fraction decomposition is,

$\frac{4}{x (x - 1)} = \frac{- 4}{x} + \frac{4}{x - 1}$

Step 3. Checking the solution.

Adding the rational expressions,

$\frac{- 4}{x} + \frac{4}{x - 1} = \frac{- 4 (x - 1) + 4 x}{x (x - 1)}$

$= \frac{- 4 x + 4 + 4 x}{x (x - 1)} = \frac{4}{x (x - 1)}$

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Write the partial fraction decomposition of each rational expression:
$\frac{4}{x (x - 1)}$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Partial Decomposition.

Step 3. Checking the solution.

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Write the partial fraction decomposition of each rational expression:4x(x-1).

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Partial Decomposition.

Step 3. Checking the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Mechanics Maths

Probability and Statistics

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write the partial fraction decomposition of each rational expression:
$\frac{4}{x (x - 1)}$ .