Chapter 11: Q. 24 (page 796)

In Problems $24$ and $25$ , write the partial fraction decomposition of each rational expression.
$\frac{3 x + 7}{(x + 3)^{2}}$

Short Answer

Expert verified

The decomposition fraction is $\frac{3 x + 7}{(x + 3)^{2}} = \frac{3}{x + 3} - \frac{2}{(x + 3)^{2}}$

Step by step solution

Step 1. Given information

An expression is given as $\frac{3 x + 7}{(x + 3)^{2}}$

Step 2. Partial fraction decomposition

Decompose the rational fraction as,

$\frac{3 x + 7}{(x + 3)^{2}} = \frac{A}{x + 3} + \frac{B}{(x + 3)^{2}}$

Now simplify,

$3 x + 7 = A (x + 3) + B = A x + B + 3 A$

Now, this is an identity. We equate the coefficients in power of x.

$\{\begin{cases} 3 = A \\ 7 = 3 A + B \end{cases}$

Now from above set we conclude that $A = 3 & B = - 2$

After substituting the values of Aand B ,we get

$\frac{3 x + 7}{(x + 3)^{2}} = \frac{3}{x + 3} - \frac{2}{(x + 3)^{2}}$

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In Problems $24$ and $25$ , write the partial fraction decomposition of each rational expression.
$\frac{3 x + 7}{(x + 3)^{2}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Partial fraction decomposition

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In Problems 24and 25, write the partial fraction decomposition of each rational expression. 3x+7(x+3)2

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

Discrete Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Pure Maths

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

In Problems $24$ and $25$ , write the partial fraction decomposition of each rational expression.
$\frac{3 x + 7}{(x + 3)^{2}}$