The algebraic expressions of the types (px+q)/(x-a)(x-b), px^{2}+qr+r/(x-a^{2})(x-b^{1}), px^{2}+qr+r/(x-a)(a^{2}+bx+c), etc. are called rational functions in which both numerator and denominator are called polynomial functions. Let f(x) and g(x) are two polynomials, then defines a rational algebraic functions, or a rational function of x. *If the degree of f(x) < the degree of g(x), then is called a proper rational function. If the**degree of f(x) the degree of g(x), then is **called an improper rational function.*

Any proper rational function *f(x)/g(x)* can be expressed as the sum of rational functions, each having a simple factor of g(x). Each such fraction is called a partial fraction, and the process of obtaining them is called the resolution, or decomposition of *f(x)/g(x)* into partial fractions.

*The resolution of f(x)/g(x) *into partial fractions depends mainly upon the nature of the factors of g(x) as discussed below.

**TYPE -1, **When denominator (g(x)) is expressed in the form of g(x) =(x –a_{1}) (x – a_{2}) (x – a_{3}) …… then, we can transform it into a sum of simple fractions i.e.

*f(x)/g(x) = A/(x-a _{1}) + A/(x-a_{2}) + A/(x-a_{3}) +……..*

Where, A, B, C…… are constants, and can be determined by equating the numerator on R.H.S. to the numerator on LHS, and then substituting x = *a _{1}+ a_{2}+a_{3……..an.}*