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 demonstrates the partial fraction decomposition for the specific form:

Where:

• \( A, B, C \) — Coefficients to be determined
• \( x \) — Variable in the expression

Explanation: The calculator verifies the decomposition by comparing both sides of the equation for given values of A, B, C, and x.

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 values for coefficients A, B, C and a value for x (x cannot be 0, -1, or -2 as these make denominators zero).

5. Frequently Asked Questions (FAQ)

Q1: What are the steps to find A, B, C?
A: Multiply both sides by the denominator, expand, and equate coefficients of like terms to solve for A, B, C.

Q2: Can this calculator solve for A, B, C automatically?
A: No, this calculator verifies the decomposition for given coefficients. You need to find A, B, C separately.

Q3: What if the denominator has repeated factors?
A: The form changes - for example, (x+1)² would require terms A/(x+1) + B/(x+1)².

Q4: Can this handle quadratic factors?
A: This specific calculator is for linear factors. Quadratic factors require different forms.

Q5: Why is partial fraction decomposition useful?
A: It simplifies integration problems and helps solve differential equations more easily.