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:
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.
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.
