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 decomposes rational expressions of the form:

Where:

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

Explanation: The calculator factors the denominator, finds the roots, and determines the coefficients that make the equation valid for all x.

3. Importance of Partial Fractions

Details: Partial fractions are essential for integration, Laplace transforms, and solving differential equations. They simplify complex algebraic expressions.

4. Using the Calculator

Tips: Enter the numerator and denominator polynomials. The denominator must be factorable into linear terms (x-r)(x-s). Use standard polynomial notation (e.g., "x^2 - x - 6").

5. Frequently Asked Questions (FAQ)

Q1: What types of denominators can be processed?
A: Currently, the calculator handles denominators that factor into distinct linear terms. Repeated roots and higher degree factors require more advanced methods.

Q2: Can I use variables other than x?
A: The calculator currently only works with the variable x.

Q3: What if my denominator doesn't factor?
A: The calculator will return an error if the denominator cannot be factored into real linear terms.

Q4: How accurate are the results?
A: Results are mathematically exact when the input follows the required format.

Q5: Can this handle more than two terms?
A: The basic version handles two distinct linear factors. Extensions can handle more complex cases.