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 Calculator Work?

The calculator solves equations of the form:

Where:

• \( N \) — Numerator (constant)
• \( a, b \) — Roots of the denominator
• \( A, B \) — Coefficients to be determined

Calculation Method: The calculator uses the Heaviside cover-up method to find the coefficients A and B by solving the system of equations derived from the original expression.

3. Importance of Partial Fractions

Applications: Partial fractions are essential for integration in calculus, solving differential equations, and performing inverse Laplace transforms in engineering.

4. Using the Calculator

Instructions: Enter the values from your denominator terms (x-a) and (x-b), and the numerator value. The calculator will compute the coefficients A and B for the partial fraction decomposition.

5. Frequently Asked Questions (FAQ)

Q1: What if my denominator has repeated roots?
A: This calculator handles distinct linear factors only. For repeated roots, additional terms with higher powers are needed.

Q2: Can this handle quadratic factors?
A: No, this calculator is designed for simple linear factors only. Quadratic factors require a different approach.

Q3: What if my denominators are equal?
A: The calculator requires distinct denominators (a ≠ b) for this method to work.

Q4: How accurate are the results?
A: Results are mathematically exact for the given inputs, rounded to 4 decimal places for display.

Q5: Can I use this for complex numbers?
A: This calculator works with real numbers only. Complex roots require complex coefficients.