Partial Fraction Coefficient Calculator

Enter Values to Calculate Missing Coefficient











Formula

The following formula is used to calculate the missing partial fraction coefficient:

\[ A = \frac{B \cdot r_2 + N \cdot r_n}{r_1} \]

Variables:

What is a Partial Fraction Coefficient?

A partial fraction coefficient is a term used in algebra and calculus to describe the coefficients of the terms in a partial fraction decomposition. Partial fraction decomposition is a method used to break down a complex rational function into simpler fractions that can be more easily integrated or manipulated. This technique is particularly useful in solving integrals and differential equations. The coefficients in the partial fraction decomposition represent the constants that multiply each term in the decomposition.

Example Calculation

Let's assume the following values:

Using the formula, we can calculate the coefficient \(A\):

\[ A = \frac{3 \cdot 5 + 2 \cdot 6}{4} = \frac{15 + 12}{4} = \frac{27}{4} = 6.75 \]

So, the coefficient \(A\) is 6.75.