Math
Partial fractions.
Definition
A technique for breaking a complex rational expression into a sum of simpler fractions, making integration or inverse Laplace transforms possible. Each factor in the denominator gets its own fraction.
How it works · 5 phases
Step by step.
- Factor the denominator completely
- Write one fraction for each factor with unknown numerator constants
- Multiply both sides by the common denominator
- Solve for the unknown constants by substituting strategic values or comparing coefficients
- Write the final decomposition
Examples
Real-world.
- 1 (2x+1)/((x+1)(x-1)) = A/(x+1) + B/(x-1)
- 2 Breaking 1/(x²-1) into 1/2·(1/(x-1) - 1/(x+1))
- 3 Used to integrate rational functions in calculus