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:

• \( a \) — Coefficient of x in numerator
• \( b \) — Constant term in numerator
• \( A, B \) — Constants to be determined
• \( c, d \) — Roots of denominator

Explanation: The calculator finds the values of A and B that make the equation true for all values of x.

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 the variable used in the expression. The calculator will show the decomposed form.

5. Frequently Asked Questions (FAQ)

Q1: When does partial fraction decomposition work?
A: It works for proper rational functions (degree of numerator less than denominator) with factorable denominators.

Q2: What about repeated roots?
A: For repeated roots like (x+c)², additional terms with higher denominators are needed.

Q3: Can this handle quadratic factors?
A: This calculator handles linear factors. Quadratic factors require a different approach.

Q4: Why is this technique important in calculus?
A: It simplifies integration of rational functions by breaking them into simpler logarithmic terms.

Q5: Are there limitations to this method?
A: Yes, it only works for factorable denominators and proper fractions (may require polynomial division first).