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 uses the partial fraction decomposition formula:

Where:

• \( P(x) \) — Numerator polynomial
• \( Q(x) \) — Denominator polynomial
• \( r, s \) — Roots of the denominator
• \( A, B \) — Coefficients to be determined

Explanation: The calculator first finds the roots of the denominator polynomial, then solves for the coefficients A and B that satisfy the equation.

3. Importance of Partial Fractions

Details: Partial fractions are essential for integration, Laplace transforms, and solving differential equations in engineering and physics.

4. Using the Calculator

Tips: Enter the coefficients of the numerator and denominator polynomials as comma-separated values (e.g., "1,2,3" for x² + 2x + 3). The denominator must be a quadratic polynomial for this calculator.

5. Frequently Asked Questions (FAQ)

Q1: What if the denominator has complex roots?
A: This calculator only handles real, distinct roots. Complex roots require a different approach.

Q2: Can I use this for higher degree polynomials?
A: This version handles quadratic denominators only. Higher degrees require more terms in the decomposition.

Q3: What if the numerator degree is higher than denominator?
A: You must first perform polynomial division before applying partial fractions.

Q4: How accurate are the results?
A: Results are mathematically exact for the given inputs, subject to floating-point precision.

Q5: What about repeated roots?
A: Repeated roots require a different form of partial fraction decomposition not handled by this calculator.