Partial fraction decomposition Calculator

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Example

Created on 2024-06-20Asked by Chloe Flores (Solvelet student)

Perform partial fraction decomposition for the rational function

\frac{3x^2 + 5x + 7}{x^3 + 2x^2 + x}

Solution

To perform partial fraction decomposition for the rational function

\frac{3x^2 + 5x + 7}{x^3 + 2x^2 + x}

: 1. Factor the denominator:

x^3 + 2x^2 + x = x(x^2 + 2x + 1) = x(x+1)^2.

2. Write the partial fraction decomposition:

\frac{3x^2 + 5x + 7}{x^3 + 2x^2 + x} = \frac{A}{x} + \frac{B}{x+1} + \frac{C}{(x+1)^2}.

3. Clear the fractions:

3x^2 + 5x + 7 = A(x+1)^2 + Bx(x+1) + Cx.

4. Solve for

A

B

, and

C

by comparing coefficients. 5. Perform the necessary algebraic operations to find the values of

A

B

, and

C

. 6. Substitute the values of

A

B

, and

C

back into the partial fraction decomposition. Solved on Solvelet with Basic AI Model

Some of the related questions asked by William Smith on Solvelet

1. Decompose the rational function

\frac{x^2 + 4x + 3}{x^3 - 1}

into partial fractions.2. Find the inverse Laplace transform of the function

F(s) = \frac{s + 2}{(s + 1)(s^2 + 1)}

DefinitionPartial Fractional decomposition is a method used to decompose a value into several simple fractions. This method is easy to integrate and solve differential equations. Example: Example: The fraction (x+1)(x+2)2x+3 can be decomposed into x+1A+x+2B.

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