Partial Fractions Calculator

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Example

Created on 2024-06-20Asked by Ella Wilson (Solvelet student)

Decompose the rational function

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

into partial fractions.

Solution

To decompose the rational function

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

into partial fractions: 1. Perform 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}.

2. Determine the values of

A

B

, and

C

by equating coefficients. 3. 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 Logan Brown on Solvelet

1. Integrate the function

\int \frac{3x + 1}{x^2 - x - 6} dx

using partial fractions.2. Evaluate the infinite series

\sum_{n=0}^{\infty} \left(\frac{1}{n} - \frac{1}{n+1}\right)

from

n = 1

\infty

using partial fractions.

DefinitionThe fractions that we get after disintegrating a rational function separately are called partial fractions. This decomposition is useful when integrating and solving equations. For example, the factorised form of (x−1)(x+2)5 will be x−1A+x+2B, and we can solve for A and B by solving a system of equations.

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