![]() In all these examples, A, B, and C are constants to be determined. Let us look at a few examples of partial fractions. Listed below in the table are partial fraction formulas (here, all variables apart from x are constants). ![]() Further, the rational expression needs to be a proper fraction to be decomposed into a partial fraction. It means, the numerator's degree of a partial fraction is always one less than the denominator's degree. And, if the denominator is a quadratic equation, then the numerator is linear. If the denominator is a linear function, the numerator is constant. The numerator of a partial fraction is not always a constant. In the above example, the numerators of partial fractions are 1 and 3. Let us learn more about partial fractions in the following sections. This rational expression, on splitting in the reverse direction involved the process of decomposition of partial fractions and results in the two partial fractions. In the normal process, we perform arithmetic operations across algebraic fractions to obtain a single rational expression. A partial fraction is a reverse of the process of the addition of rational expressions. While decomposition, generally, the denominator is an algebraic expression, and this expression is factorized to facilitate the process of generating partial fractions. Generally, fractions with algebraic expressions are difficult to solve and hence we use the concepts of partial fractions to split the fractions into numerous subfractions. ![]() Partial Fractions are the fractions that are formed when a complex rational expression is split into two or more simpler fractions. ![]()
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