Partial Fractions

 

 

Contents

 

Partial Fractions

 

Distinct Linear Factors

1 2

Repeated Linear Factors

 

Quadratic Factors

 

Improper Fractions

 

Quiz

 

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Distinct Linear Factors
 
 
 
In a proper fraction, every linear factor in the denominator has a partial fraction in the form
,
where A, a and b are constants.
 
 
 
Take an example:
Express 
              
                              in partial factions.
 
Let 
        
                           
                    - x - 26 = A (x - 2) + B (x + 5)
 
Let x=2,    7B = -28
                 B = -4
 
Let x= -5,  -7A = -21
                   A = 3
 
The above two steps uses the idea of algebraic identities.
 
Hence,