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 algebra.

2. How Does the Calculator Work?

The calculator solves equations of the form:

Where:

• \( a, b \) — Coefficients from the numerator
• \( c, d, e, f \) — Coefficients from the denominator factors
• \( A, B \) — Partial fraction coefficients to be determined
• \( x \) — Variable in the expression

Explanation: The calculator solves for A and B by equating coefficients and solving the resulting system of equations.

3. Importance of Partial Fractions

Details: Partial fractions are essential for integration in calculus, solving differential equations, and simplifying complex algebraic expressions.

4. Using the Calculator

Tips: Enter all coefficients (a, b, c, d, e, f) as real numbers. The calculator will return the values of A and B for the partial fraction decomposition.

5. Frequently Asked Questions (FAQ)

Q1: What if the denominator can't be factored?
A: This calculator only works for denominators that can be factored into linear terms. For irreducible quadratics, different forms are needed.

Q2: Can this handle repeated roots?
A: This version handles distinct linear factors. For repeated roots, additional terms with higher powers are needed.

Q3: What if I get division by zero?
A: This occurs when (c*f - d*e) = 0, meaning the denominator factors are not distinct. The partial fraction form would need adjustment.

Q4: Can I use this for complex numbers?
A: The calculator is designed for real coefficients. Complex coefficients would require complex arithmetic.

Q5: How accurate are the results?
A: Results are accurate to 4 decimal places. For exact fractions, symbolic computation would be needed.