Partial Fractions Calculator
Decompose rational expressions into partial fractions for easier integration and simplification.
Input Rational Expression
Example: (x + 1)*(x + 2) for denominator
Theory & Formula
Partial Fraction Decomposition
Partial fraction decomposition is a method to break down complex rational expressions into simpler fractions. This technique is particularly useful for integration.
Method
For linear factors: Split the fraction into sum of simpler fractions
\(\frac{P(x)}{(x-a)(x-b)} = \frac{A}{x-a} + \frac{B}{x-b}\)Example
\(\frac{5x + 7}{(x+1)(x+2)} = \frac{A}{x+1} + \frac{B}{x+2}\)\(5x + 7 = A(x+2) + B(x+1)\)\(\text{Solving: } A = 2, B = 3\)\(\frac{5x + 7}{(x+1)(x+2)} = \frac{2}{x+1} + \frac{3}{x+2}\)