A partial fraction is a mathematical technique used to break down a rational function into simpler, smaller fractions. It is useful in solving integration problems and simplifying complex expressions.
We use partial fractions to simplify complex expressions and make them easier to work with. This technique allows us to break down a single, complicated fraction into smaller, more manageable fractions.
To find the partial fraction of an expression, we first factor the denominator into linear and irreducible quadratic factors. Then, we set up a system of equations and solve for the unknown coefficients using algebraic techniques.
There are two types of partial fractions: proper and improper. A proper partial fraction has a degree of the numerator less than the degree of the denominator, while an improper partial fraction has a degree of the numerator greater than or equal to the degree of the denominator.
Yes, partial fractions can be used in various real-world applications such as engineering, physics, and economics. It is particularly useful in solving differential equations and in circuit analysis.