Enter the original rational function and the numerators and denominators of the decomposed fractions into the calculator to determine the fractional decomposition.
Fractional Decomposition Formula
The following formula is used to calculate the fractional decomposition of a rational function.
A/B = (A1/B1) + (A2/B2) + ... + (An/Bn)
Variables:
- A/B is the original rational function
- A1, A2, …, An are the numerators of the decomposed fractions
- B1, B2, …, Bn are the denominators of the decomposed fractions
To calculate the fractional decomposition, divide the original rational function into simpler fractions whose sum is equal to the original function. The numerators and denominators of these simpler fractions are determined by the factors of the original function’s denominator.
What is a Fractional Decomposition?
Fractional decomposition is a mathematical process used to break down complex fractions or rational expressions into simpler parts, often for the purpose of integration or simplification. It involves expressing the fraction as a sum of simpler fractions with linear or quadratic denominators. This method is particularly useful in calculus and algebra for solving equations and integrating functions.
How to Calculate Fractional Decomposition?
The following steps outline how to calculate the Fractional Decomposition using the given formula:
- First, identify the original rational function A/B.
- Next, decompose the rational function into individual fractions.
- For each decomposed fraction, identify the numerator (A1, A2, …, An) and the denominator (B1, B2, …, Bn).
- Write the decomposed fractions in the form (A1/B1) + (A2/B2) + … + (An/Bn).
- Finally, simplify the expression if possible.
Example Problem:
Use the following variables as an example problem to test your knowledge:
A/B = 3/4
A1 = 1, B1 = 2
A2 = 2, B2 = 3
A3 = 1, B3 = 6
