Partial fractions decomposition is a mathematical method used to decompose a rational function into simpler fractions. It involves breaking down a fraction with a polynomial numerator and denominator into smaller fractions with simpler expressions in the numerator and denominator.
Partial fractions decomposition is useful in solving integration problems, especially those involving rational functions. It helps in simplifying complex fractions and making them easier to integrate.
To perform partial fractions decomposition, you first need to factor the denominator of the rational function. Then, you set up an equation with unknown coefficients for each factor in the denominator. You then solve for these coefficients by equating the original rational function with the sum of the decomposed fractions.
Yes, all rational functions can be decomposed using partial fractions. However, some may require more complicated decomposition methods such as using partial fractions with repeated linear factors or quadratic factors.
Partial fractions decomposition can be applied in various fields such as engineering, physics, and economics. For example, it can be used to model the behavior of a system, solve differential equations, or calculate areas under curves. It can also be applied in finance to calculate present values and future cash flows.