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
• \( A, B \) — Coefficients to be determined
• \( r, s \) — Roots of the denominator

Explanation: The calculator factors the denominator, finds its roots, and solves for the unknown coefficients in the partial fraction expansion.

3. Importance of Partial Fractions

Details: Partial fractions are essential for integration of rational functions, solving differential equations, and simplifying complex algebraic expressions.

4. Using the Calculator

Tips: Enter the coefficients of the numerator and denominator polynomials as comma-separated values. For example, for x²+2x+1, enter "1,2,1".

5. Frequently Asked Questions (FAQ)

Q1: What types of denominators does this support?
A: This calculator handles denominators that factor into distinct linear terms (x-r)(x-s).

Q2: How do I enter the polynomial coefficients?
A: Enter them in order from highest degree to lowest. For 2x³+3x+1, enter "2,0,3,1".

Q3: What if my denominator has repeated roots?
A: This calculator doesn't handle repeated roots. The method would require different partial fraction terms.

Q4: Can this handle higher degree polynomials?
A: The current implementation is designed for quadratic denominators that factor into two distinct linear terms.

Q5: What if I get complex roots?
A: This calculator only works with real roots. Complex roots would require a different approach.