1. What is Partial Fraction Decomposition?

Partial fraction decomposition is a technique used to break down complex rational expressions into simpler fractions that are easier to work with, especially in calculus and differential equations.

2. How Does the Solver Work?

The calculator solves equations of the form:

Where:

• \( num \) — Numerator of the original fraction
• \( a, b \) — Distinct roots of the denominator
• \( A, B \) — Coefficients to be determined

Method: The solver uses the Heaviside cover-up method to find the coefficients A and B by solving the system of equations derived from equating the numerators.

3. Importance of Partial Fractions

Applications: Partial fraction decomposition is essential for integration of rational functions, solving differential equations using Laplace transforms, and simplifying complex algebraic expressions.

4. Using the Calculator

Instructions: Enter the numerator value and the two distinct roots of the denominator. The calculator will compute the coefficients A and B for the partial fraction decomposition.

5. Frequently Asked Questions (FAQ)

Q1: What if the denominator has repeated roots?
A: This calculator handles only distinct linear factors. For repeated roots, the decomposition includes additional terms.

Q2: Can this handle quadratic factors?
A: No, this calculator is designed only for distinct linear factors in the denominator.

Q3: What if the roots are equal?
A: The calculator requires distinct roots (a ≠ b). For equal roots, a different decomposition method is needed.

Q4: How accurate are the results?
A: Results are accurate to 4 decimal places. For exact fractions, symbolic computation may be needed.

Q5: Can I use this for improper fractions?
A: No, the numerator degree must be less than the denominator degree. Perform polynomial division first if needed.