Partial fraction Shortcut Methods and Trick (आंशिक भिन्न )

In this article we are going to discuss about solving approach of partial fraction questions.
Partial fraction is widely used in integration problems in 12th level mathematics also in various competitive examinations.

General method

(px+q)/(x−a)(x−b).=A/(x−a).+B/(x−b)

For example:
Ques-:          2x + 3                                        
                   (x+1)(x-3)
Solution:  

                             2x+3         ------------(1)
                        (x+1)(x-3)
Seperating the equation
                 2x+3     =     A     +    B             -------(2)
               (x+1)(x-3)      (x+1)    (x-3)

               2x+3=A(x-3)+B(x+1)............(3)
*for.     (x+1)=0.   We have    x=-1
            On substituting 2+3=A(-1-3)
             1=-4A ,    A= -1/4
* Again if (x-3)=0 then x=3 again substituting
      2(3)+3=B(3+1)
      9=4B, B =9/4
A and B value equation (2)partial fraction is 
        -1       +      9     
     4(x+1)      4(x-3)  

Shortcut Method:
Ques-:          2x + 3                                        
                   (x+1)(x-3)

                          2x+3         ------------(1)
                        (x+1)(x-3)
Seperating the equation

                 2x+3     =     A     +    B             -------(2)
               (x+1)(x-3)      (x+1)    (x-3)

Substituting the obtained values.
    -1       +      9     
     4(x+1)      4(x-3)  

This way we can easily solve any partial fraction question in short time

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