1. What is Partial Fractions Decomposition?

Partial fractions decomposition is a technique used to break down complex rational expressions into simpler fractions that are easier to work with in calculus and algebra.

2. How Does the Calculator Work?

The calculator solves equations of the form:

Which leads to the equation:

The calculator solves for A and B by:

• Expanding the left side: (A + B)x - A
• Setting up equations by comparing coefficients
• Solving the system of equations

3. Importance of Partial Fractions

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

4. Using the Calculator

Tips: Enter the coefficients from the numerator (x coefficient and constant term). The denominator is assumed to be x(x-1) in this specific calculator.

5. Frequently Asked Questions (FAQ)

Q1: What types of denominators can be decomposed?
A: This calculator handles distinct linear factors (x)(x-1). Other forms require different approaches.

Q2: Can this handle quadratic factors?
A: No, this specific calculator only handles linear factors. Quadratic factors require different decomposition methods.

Q3: What if the numerator degree is higher than denominator?
A: Polynomial long division must be performed first before partial fractions can be applied.

Q4: How is this used in calculus?
A: Partial fractions make rational functions easier to integrate, especially when using techniques like logarithmic integration.

Q5: Can this handle repeated roots?
A: This specific calculator doesn't handle repeated roots, which require additional terms in the decomposition.